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log((e^(sin(2*x))*sin(x)^(3))/(tan(4*x)*x^(1/3)))

  • Как пользоваться?

  • Производная:
  • Производная e^x*cos(x)
  • Производная 1/x+4*x
  • Производная -1/(x^2)
  • Производная 2*e^(2*x)-10*e^x+8

  • Идентичные выражения

  • log((e^(sin(два *x))*sin(x)^(три))/(tan(четыре *x)*x^(один / три)))
  • логарифм от ((e в степени ( синус от (2 умножить на x)) умножить на синус от (x) в степени (3)) делить на ( тангенс от (4 умножить на x) умножить на x в степени (1 делить на 3)))
  • логарифм от ((e в степени ( синус от (два умножить на x)) умножить на синус от (x) в степени (три)) делить на ( тангенс от (четыре умножить на x) умножить на x в степени (один делить на три)))
  • log((e(sin(2*x))*sin(x)(3))/(tan(4*x)*x(1/3)))
  • logesin2*x*sinx3/tan4*x*x1/3
  • log((e^(sin(2x))sin(x)^(3))/(tan(4x)x^(1/3)))
  • log((e(sin(2x))sin(x)(3))/(tan(4x)x(1/3)))
  • logesin2xsinx3/tan4xx1/3
  • loge^sin2xsinx^3/tan4xx^1/3
  • log((e^(sin(2*x))*sin(x)^(3)) разделить на (tan(4*x)*x^(1 разделить на 3)))

  • Похожие выражения

  • log((e^(sin(2*x))*sinx^(3))/(tan(4*x)*x^(1/3)))
Производная функции/ log((e^(sin(2*x))*sin(x)^(3))/(tan(4*x)*x^(1/3)))

Производная log((e^(sin(2*x))*sin(x)^(3))/(tan(4*x)*x^(1/3)))

Функция f() - производная -го порядка в точке
v

График:

от до

Кусочно-заданная:

Решение

Вы ввели [src] 
   / sin(2*x)    3   \
   |e        *sin (x)|
log|-----------------|
   |           3 ___ |
   \  tan(4*x)*\/ x  /
$$\log{\left(\frac{e^{\sin{\left(2 x \right)}} \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} \right)}$$ 
  /   / sin(2*x)    3   \\
d |   |e        *sin (x)||
--|log|-----------------||
dx|   |           3 ___ ||
  \   \  tan(4*x)*\/ x  //
$$\frac{d}{d x} \log{\left(\frac{e^{\sin{\left(2 x \right)}} \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} \right)}$$
Преобразовать
Подробное решение

  1. Заменим .

  2. Производная является .

  3. Затем примените цепочку правил. Умножим на :

    1. Применим правило производной частного:

      и .

      Чтобы найти :

      1. Применяем правило производной умножения:

        ; найдём :

        1. Заменим .

        2. В силу правила, применим: получим

        3. Затем примените цепочку правил. Умножим на :

          1. Производная синуса есть косинус:

          В результате последовательности правил:

        ; найдём :

        1. Заменим .

        2. Производная само оно.

        3. Затем примените цепочку правил. Умножим на :

          1. Заменим .

          2. Производная синуса есть косинус:

          3. Затем примените цепочку правил. Умножим на :

            1. Производная произведения константы на функцию есть произведение этой константы на производную данной функции.

              1. В силу правила, применим: получим

              Таким образом, в результате:

            В результате последовательности правил:

          В результате последовательности правил:

        В результате:

      Чтобы найти :

      1. Применяем правило производной умножения:

        ; найдём :

        1. В силу правила, применим: получим

        ; найдём :

        1. Перепишем функции, чтобы дифференцировать:

        2. Применим правило производной частного:

          и .

          Чтобы найти :

          1. Заменим .

          2. Производная синуса есть косинус:

          3. Затем примените цепочку правил. Умножим на :

            1. Производная произведения константы на функцию есть произведение этой константы на производную данной функции.

              1. В силу правила, применим: получим

              Таким образом, в результате:

            В результате последовательности правил:

          Чтобы найти :

          1. Заменим .

          2. Производная косинус есть минус синус:

          3. Затем примените цепочку правил. Умножим на :

            1. Производная произведения константы на функцию есть произведение этой константы на производную данной функции.

              1. В силу правила, применим: получим

              Таким образом, в результате:

            В результате последовательности правил:

          Теперь применим правило производной деления:

        В результате:

      Теперь применим правило производной деления:

    В результате последовательности правил:

  4. Теперь упростим:

Ответ:

График
Построить график f(x)
Построить график f'(x)
Первая производная [src] 
      /                                                                                             3    /  3 ___ /         2     \   tan(4*x)\  sin(2*x)\                    
      |                                                                                          sin (x)*|- \/ x *\4 + 4*tan (4*x)/ - --------|*e        |                    
      |                                                                                                  |                                2/3 |          |                    
3 ___ |     3          1                  sin(2*x)        2          1                sin(2*x)           \                             3*x    /          |  -sin(2*x)         
\/ x *|2*sin (x)*--------------*cos(2*x)*e         + 3*sin (x)*--------------*cos(x)*e         + --------------------------------------------------------|*e         *tan(4*x)
      |          3 ___                                         3 ___                                                   2/3    2                          |                    
      \          \/ x *tan(4*x)                                \/ x *tan(4*x)                                         x   *tan (4*x)                     /                    
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                      3                                                                                       
                                                                                   sin (x)
$$\frac{\sqrt[3]{x} \left(2 \cdot \frac{1}{\sqrt[3]{x} \tan{\left(4 x \right)}} e^{\sin{\left(2 x \right)}} \sin^{3}{\left(x \right)} \cos{\left(2 x \right)} + 3 \cdot \frac{1}{\sqrt[3]{x} \tan{\left(4 x \right)}} e^{\sin{\left(2 x \right)}} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{\left(- \sqrt[3]{x} \left(4 \tan^{2}{\left(4 x \right)} + 4\right) - \frac{\tan{\left(4 x \right)}}{3 x^{\frac{2}{3}}}\right) e^{\sin{\left(2 x \right)}} \sin^{3}{\left(x \right)}}{x^{\frac{2}{3}} \tan^{2}{\left(4 x \right)}}\right) e^{- \sin{\left(2 x \right)}} \tan{\left(4 x \right)}}{\sin^{3}{\left(x \right)}}$$
Упростить
Вторая производная [src] 
                                                                                                                                                                                                                                                                                                                                                        /                /       2     \                                     \                                                                                                                                                                                                                                                                                                                                                                                                                                                             
    /                               /tan(4*x)      3 ___ /       2     \\       \                                                                                                                                                                                                                2    /tan(4*x)      3 ___ /       2     \\        2    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |         2    /       2     \ /tan(4*x)      3 ___ /       2     \\        2    /tan(4*x)      3 ___ /       2     \\              /tan(4*x)      3 ___ /       2     \\                                                /tan(4*x)      3 ___ /       2     \\          /                               /tan(4*x)      3 ___ /       2     \\       \                            /                               /tan(4*x)      3 ___ /       2     \\       \
    |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                                                                                                                                                                                                           2*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   2*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   24*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   6*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   9*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)*sin(x)                                  |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)   |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                            |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|
    |                               |   2/3                             |       |                                                                                                                            /       /       2     \\              /       /       2     \\                           |   2/3                             |             |     5/3             2/3                                            |                              |   2/3                             |             |   2/3                             |              |   2/3                             |                                                |   2/3                             |          |                               |   2/3                             |       |                            |                               |   2/3                             |       |
    |                               \  x                                /       |                    2            2            2         2            2                                                 2    |1   12*\1 + tan (4*x)/|              |1   12*\1 + tan (4*x)/|                           \  x                                /             \    x               x                                               /                              \  x                                /             \  x                                /              \  x                                /                                                \  x                                /          |                               \  x                                /       |            /       2     \ |                               \  x                                /       |
  2*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(2*x)   - 54*cos (x) + 27*sin (x) - 36*cos (2*x)*sin (x) + 36*sin (x)*sin(2*x) - 108*cos(x)*cos(2*x)*sin(x) + 6*sin (x)*|- + ------------------|*cos(2*x) + 9*|- + ------------------|*cos(x)*sin(x) - ----------------------------------------------- + -------------------------------------------------------------------------------- - ---------------------------------------------------------------- + -------------------------------------------------------- + -----------------------------------------------------   9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------   |9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(x)   4*\1 + tan (4*x)/*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|
    |                                              3 ___                        |                                                                                                                            \x        tan(4*x)     /              \x        tan(4*x)     /                                   4/3                                                              3 ___                                                                     3 ___    2                                                      3 ___                                                     3 ___                                                                             3 ___                           |                                              3 ___                        |                            |                                              3 ___                        |
    \                                              \/ x *tan(4*x)               /                                                                                                                                                                                                                            x   *tan(4*x)                                                     \/ x *tan(4*x)                                                            \/ x *tan (4*x)                                                 \/ x *tan(4*x)                                            \/ x *tan(4*x)                                                                    \/ x *tan(4*x)                  \                                              \/ x *tan(4*x)               /                            \                                              \/ x *tan(4*x)               /
- ---------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------- - ------------------------------------------------------------------------------------ + -----------------------------------------------------------------------------------------------
                                             3                                                                                                                                                                                                                                                                                                       9*sin(x)                                                                                                                                                                                                                                                                                              9*x                                                                              sin(x)                                                                                     3*tan(4*x)                                          
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                           sin(x)
$$\frac{- \frac{2 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(2 x \right)}}{3} + \frac{4 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right)}{3 \tan{\left(4 x \right)}} - \frac{\left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{6 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)} - 36 \sin^{2}{\left(x \right)} \cos^{2}{\left(2 x \right)} + 9 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 36 \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} - 108 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)} + 27 \sin^{2}{\left(x \right)} - 54 \cos^{2}{\left(x \right)} + \frac{6 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{24 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} + \frac{9 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{2 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}}}{9 \sin{\left(x \right)}} + \frac{6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}}{9 x}}{\sin{\left(x \right)}}$$
Упростить
Третья производная [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /                /       2     \                                     \             /     /       2     \                                          2       /       2     \                                                \                                                                                                                                                                                                                                                                                                                       /                /       2     \                                     \                                                                                                                                                                                                /                /       2     \                                     \                                                                                    /                /       2     \                                     \                                                                                                                                                          2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             /                                                                                                                                                                                                                                                           /                /       2     \                                     \                                                                                                                                                                                      \     /                                                                                                                                                                                                                                                           /                /       2     \                                     \                                                                                                                                                                                      \            /                                                                                                                                                                                                                                                           /                /       2     \                                     \                                                                                                                                                                                      \                                                                                                                                                                                                                                                                                           /                                                                                                                                                                                                                                                           /                /       2     \                                     \                                                                                                                                                                                      \                                                                                                                                                                                                                                                                                                    
                                 /                               /tan(4*x)      3 ___ /       2     \\       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               3    /tan(4*x)      3 ___ /       2     \\        3    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |        3    |  36*\1 + tan (4*x)/   5*tan(4*x)        3 ___ /       2     \    432*\1 + tan (4*x)/*tan(4*x)        3 ___    2      /       2     \|         3    /tan(4*x)      3 ___ /       2     \\                                                                                                                                                                            3    /       2     \ /tan(4*x)      3 ___ /       2     \\         3    /       2     \ |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |         2    /tan(4*x)      3 ___ /       2     \\                3    /tan(4*x)      3 ___ /       2     \\                  3    /tan(4*x)      3 ___ /       2     \\                  3    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |                  2         3    /tan(4*x)      3 ___ /       2     \\         2    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |                2    /tan(4*x)      3 ___ /       2     \\                3    /       2     \ /tan(4*x)      3 ___ /       2     \\       /       2     \     3    /tan(4*x)      3 ___ /       2     \\                                                         2    /       2     \ /tan(4*x)      3 ___ /       2     \\                 3    /       2     \ /tan(4*x)      3 ___ /       2     \\                   2    /tan(4*x)      3 ___ /       2     \\                               /                               /tan(4*x)      3 ___ /       2     \\       \     /                               /tan(4*x)      3 ___ /       2     \\       \                               /                               /tan(4*x)      3 ___ /       2     \\       \             /                               /tan(4*x)      3 ___ /       2     \\       \     /                               /tan(4*x)      3 ___ /       2     \\       \              |                                                                                                                                                                                                    2    /tan(4*x)      3 ___ /       2     \\        2    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |         2    /       2     \ /tan(4*x)      3 ___ /       2     \\        2    /tan(4*x)      3 ___ /       2     \\              /tan(4*x)      3 ___ /       2     \\              |     |                                                                                                                                                                                                    2    /tan(4*x)      3 ___ /       2     \\        2    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |         2    /       2     \ /tan(4*x)      3 ___ /       2     \\        2    /tan(4*x)      3 ___ /       2     \\              /tan(4*x)      3 ___ /       2     \\              |            |                                                                                                                                                                                                    2    /tan(4*x)      3 ___ /       2     \\        2    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |         2    /       2     \ /tan(4*x)      3 ___ /       2     \\        2    /tan(4*x)      3 ___ /       2     \\              /tan(4*x)      3 ___ /       2     \\              |                                                             /                               /tan(4*x)      3 ___ /       2     \\       \                                      /                               /tan(4*x)      3 ___ /       2     \\       \                              |                                                                                                                                                                                                    2    /tan(4*x)      3 ___ /       2     \\        2    |  tan(4*x)   12*\1 + tan (4*x)/       3 ___ /       2     \         |         2    /       2     \ /tan(4*x)      3 ___ /       2     \\        2    /tan(4*x)      3 ___ /       2     \\              /tan(4*x)      3 ___ /       2     \\              |     /                               /tan(4*x)      3 ___ /       2     \\       \                            /                               /tan(4*x)      3 ___ /       2     \\       \                     /                               /tan(4*x)      3 ___ /       2     \\       \       
                                 |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                                                                                                                                                                                                                                                                      /                                            2                    \                                                                    /                                            2                    \                                                                                                                                                                                                                                                         27*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   8*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   2*sin (x)*|- ------------------ + ---------- + 1728*\/ x *\1 + tan (4*x)/  + ---------------------------- + 3456*\/ x *tan (4*x)*\1 + tan (4*x)/|   10*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|                                                                                                                                                                     576*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   96*sin (x)*\1 + tan (4*x)/*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   36*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)   36*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*sin(2*x)   24*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   24*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|*cos(2*x)   36*cos (2*x)*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   36*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|*cos(x)   54*cos (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)   96*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   864*\1 + tan (4*x)/ *sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|                                                  432*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)   288*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   108*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)*cos(2*x)               |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|     |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                               |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|             |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|     |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|              |                                                                                                                                                                                               2*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   2*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   24*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   6*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   9*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)*sin(x)|     |                                                                                                                                                                                               2*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   2*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   24*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   6*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   9*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)*sin(x)|            |                                                                                                                                                                                               2*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   2*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   24*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   6*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   9*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)*sin(x)|                                                             |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                                      |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                              |                                                                                                                                                                                               2*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|   2*sin (x)*|- -------- + ------------------ + 144*\/ x *\1 + tan (4*x)/*tan(4*x)|   24*sin (x)*\1 + tan (4*x)/*|-------- + 12*\/ x *\1 + tan (4*x)/|   6*sin (x)*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(2*x)   9*|-------- + 12*\/ x *\1 + tan (4*x)/|*cos(x)*sin(x)|     |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                            |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|                     |                               |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)|       
                                 |                               |   2/3                             |       |                                                 3                 /       /       2     \\                                                                                                                   3    /       2     \         3                          |                             /       2     \      /       2     \|                     /       /       2     \\                       |                             /       2     \      /       2     \|                  2         3                           /       /       2     \\         2                        /       /       2     \\                                                                               3    /       2     \                       |   2/3                             |             |     5/3             2/3                                            |             |          5/3              8/3                                                 2/3                                                   |              |   2/3                             |          2                                  /       /       2     \\                          2         3    /       2     \          2    /       2     \                                      |   2/3                             |                              |     5/3             2/3                                            |              |   2/3                             |                     |   2/3                             |                       |   2/3                             |                       |     5/3             2/3                                            |                                 |   2/3                             |              |     5/3             2/3                                            |                     |   2/3                             |                                     |   2/3                             |                                |   2/3                             |           2    /       2     \                                               |   2/3                             |                                      |   2/3                             |                        |   2/3                             |                               |                               |   2/3                             |       |     |                               |   2/3                             |       |                               |                               |   2/3                             |       |             |                               |   2/3                             |       |     |                               |   2/3                             |       |              |                                                                                                                /       /       2     \\              /       /       2     \\                           |   2/3                             |             |     5/3             2/3                                            |                              |   2/3                             |             |   2/3                             |              |   2/3                             |              |     |                                                                                                                /       /       2     \\              /       /       2     \\                           |   2/3                             |             |     5/3             2/3                                            |                              |   2/3                             |             |   2/3                             |              |   2/3                             |              |            |                                                                                                                /       /       2     \\              /       /       2     \\                           |   2/3                             |             |     5/3             2/3                                            |                              |   2/3                             |             |   2/3                             |              |   2/3                             |              |                                                             |                               |   2/3                             |       |                                      |                               |   2/3                             |       |                              |                                                                                                                /       /       2     \\              /       /       2     \\                           |   2/3                             |             |     5/3             2/3                                            |                              |   2/3                             |             |   2/3                             |              |   2/3                             |              |     |                               |   2/3                             |       |                            |                               |   2/3                             |       |                     |                               |   2/3                             |       |       
                                 |                               \  x                                /       |            3             3         3      27*sin (x)         3    |1   12*\1 + tan (4*x)/|          2                    3                      2                             2         2             324*sin (x)*\1 + tan (4*x)/   36*sin (x)*sin(2*x)         2    |      1          2        72*\1 + tan (4*x)/    6*\1 + tan (4*x)/|                3    |1   12*\1 + tan (4*x)/|                  3    |      1          2        72*\1 + tan (4*x)/    6*\1 + tan (4*x)/|            36*cos (2*x)*sin (x)         2         3    |1   12*\1 + tan (4*x)/|   54*cos (x)*sin(x)         2    |1   12*\1 + tan (4*x)/|                 3                               2                      432*sin (x)*\1 + tan (4*x)/*sin(2*x)              \  x                                /             \    x               x                                               /             \         x                x                                                   x                                                      /              \  x                                /   108*sin (x)*cos(x)*cos(2*x)          2    |1   12*\1 + tan (4*x)/|                   432*cos (2*x)*sin (x)*\1 + tan (4*x)/   648*cos (x)*\1 + tan (4*x)/*sin(x)                               \  x                                /                              \    x               x                                               /              \  x                                /                     \  x                                /                       \  x                                /                       \    x               x                                               /                                 \  x                                /              \    x               x                                               /                     \  x                                /                                     \  x                                /                                \  x                                /   1296*sin (x)*\1 + tan (4*x)/*cos(x)*cos(2*x)                               \  x                                /                                      \  x                                /                        \  x                                /                        2      |                               \  x                                /       |     |                               \  x                                /       |               /       2     \ |                               \  x                                /       |        2    |                               \  x                                /       |     |                               \  x                                /       |              |        2            2            2         2            2                                                 2    |1   12*\1 + tan (4*x)/|              |1   12*\1 + tan (4*x)/|                           \  x                                /             \    x               x                                               /                              \  x                                /             \  x                                /              \  x                                /              |     |        2            2            2         2            2                                                 2    |1   12*\1 + tan (4*x)/|              |1   12*\1 + tan (4*x)/|                           \  x                                /             \    x               x                                               /                              \  x                                /             \  x                                /              \  x                                /              |            |        2            2            2         2            2                                                 2    |1   12*\1 + tan (4*x)/|              |1   12*\1 + tan (4*x)/|                           \  x                                /             \    x               x                                               /                              \  x                                /             \  x                                /              \  x                                /              |            /tan(4*x)      3 ___ /       2     \\            |                               \  x                                /       |                      /       2     \ |                               \  x                                /       |              /       2     \ |        2            2            2         2            2                                                 2    |1   12*\1 + tan (4*x)/|              |1   12*\1 + tan (4*x)/|                           \  x                                /             \    x               x                                               /                              \  x                                /             \  x                                /              \  x                                /              |     |                               \  x                                /       |            /       2     \ |                               \  x                                /       |     /       2     \ |                               \  x                                /       |       
                               2*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|   - 162*cos (x) - 216*cos (2*x)*sin (x) - ---------- - 27*sin (x)*|- + ------------------| + 567*sin (x)*cos(x) + 702*sin (x)*cos(2*x) - 972*cos (x)*cos(2*x)*sin(x) - 972*cos (2*x)*sin (x)*cos(x) - --------------------------- - ------------------- - 36*sin (x)*|-72 + -- - 72*tan (4*x) + ------------------- + -----------------|*cos(x) - 36*sin (x)*|- + ------------------|*sin(2*x) - 24*sin (x)*|-72 + -- - 72*tan (4*x) + ------------------- + -----------------|*cos(2*x) + -------------------- + 36*cos (2*x)*sin (x)*|- + ------------------| + ----------------- + 54*cos (x)*|- + ------------------|*sin(x) + 648*sin (x)*cos(2*x)*sin(2*x) + 972*sin (x)*cos(x)*sin(2*x) - ------------------------------------ - ------------------------------------------------ - -------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------ + --------------------------- + 108*sin (x)*|- + ------------------|*cos(x)*cos(2*x) + ------------------------------------- + ---------------------------------- - ----------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------- - --------------------------------------------------------- - --------------------------------------------------------- + ------------------------------------------------------------------------------------------ + ---------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------- + ---------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------------------- - ------------------------------------------------------------------------ - -------------------------------------------------------------------------- + -----------------------------------------------------------------   4*cos (2*x)*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|   4*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*sin(2*x)   32*\1 + tan (4*x)/*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|   4*cos (x)*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|   4*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(2*x)   2*|- 54*cos (x) + 27*sin (x) - 36*cos (2*x)*sin (x) + 36*sin (x)*sin(2*x) - 108*cos(x)*cos(2*x)*sin(x) + 6*sin (x)*|- + ------------------|*cos(2*x) + 9*|- + ------------------|*cos(x)*sin(x) - ----------------------------------------------- + -------------------------------------------------------------------------------- - ---------------------------------------------------------------- + -------------------------------------------------------- + -----------------------------------------------------|   2*|- 54*cos (x) + 27*sin (x) - 36*cos (2*x)*sin (x) + 36*sin (x)*sin(2*x) - 108*cos(x)*cos(2*x)*sin(x) + 6*sin (x)*|- + ------------------|*cos(2*x) + 9*|- + ------------------|*cos(x)*sin(x) - ----------------------------------------------- + -------------------------------------------------------------------------------- - ---------------------------------------------------------------- + -------------------------------------------------------- + -----------------------------------------------------|*cos(x)   4*|- 54*cos (x) + 27*sin (x) - 36*cos (2*x)*sin (x) + 36*sin (x)*sin(2*x) - 108*cos(x)*cos(2*x)*sin(x) + 6*sin (x)*|- + ------------------|*cos(2*x) + 9*|- + ------------------|*cos(x)*sin(x) - ----------------------------------------------- + -------------------------------------------------------------------------------- - ---------------------------------------------------------------- + -------------------------------------------------------- + -----------------------------------------------------|*cos(2*x)   |-------- + 12*\/ x *\1 + tan (4*x)/|*sin(x)   4*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(x)*cos(2*x)   16*\1 + tan (4*x)/*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(2*x)   8*\1 + tan (4*x)/*|- 54*cos (x) + 27*sin (x) - 36*cos (2*x)*sin (x) + 36*sin (x)*sin(2*x) - 108*cos(x)*cos(2*x)*sin(x) + 6*sin (x)*|- + ------------------|*cos(2*x) + 9*|- + ------------------|*cos(x)*sin(x) - ----------------------------------------------- + -------------------------------------------------------------------------------- - ---------------------------------------------------------------- + -------------------------------------------------------- + -----------------------------------------------------|   2*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(x)   8*\1 + tan (4*x)/*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|   8*\1 + tan (4*x)/*|9*cos(x) + 6*cos(2*x)*sin(x) - --------------------------------------------|*cos(x)
                                 |                                              3 ___                        |                                               x                   \x        tan(4*x)     /                                                                                                                      tan(4*x)                     x                       |       2                          2                 x*tan(4*x)   |                     \x        tan(4*x)     /                       |       2                          2                 x*tan(4*x)   |                     x                                  \x        tan(4*x)     /           x                      \x        tan(4*x)     /                                                                                      tan(4*x)                                  3 ___                                                               4/3                                                                                                                3 ___                                                                                               7/3                                           x                            \x        tan(4*x)     /                                  tan(4*x)                              tan(4*x)                                          3 ___                                                                              3 ___    2                                                                       4/3                                                       3 ___                                                        4/3                                                                        3 ___                                                                        3 ___                                                                       3 ___                                                                      3 ___                                                          4/3    2                                                          3 ___    3                                                    tan(4*x)                                                 3 ___    2                                                                  3 ___    2                                                                3 ___                                                 |                                              3 ___                        |     |                                              3 ___                        |                               |                                              3 ___                        |             |                                              3 ___                        |     |                                              3 ___                        |              |                                                                                                                \x        tan(4*x)     /              \x        tan(4*x)     /                                   4/3                                                              3 ___                                                                     3 ___    2                                                      3 ___                                                     3 ___                            |     |                                                                                                                \x        tan(4*x)     /              \x        tan(4*x)     /                                   4/3                                                              3 ___                                                                     3 ___    2                                                      3 ___                                                     3 ___                            |            |                                                                                                                \x        tan(4*x)     /              \x        tan(4*x)     /                                   4/3                                                              3 ___                                                                     3 ___    2                                                      3 ___                                                     3 ___                            |            |   2/3                             |            |                                              3 ___                        |                                      |                                              3 ___                        |                              |                                                                                                                \x        tan(4*x)     /              \x        tan(4*x)     /                                   4/3                                                              3 ___                                                                     3 ___    2                                                      3 ___                                                     3 ___                            |     |                                              3 ___                        |                            |                                              3 ___                        |                     |                                              3 ___                        |       
                                 \                                              \/ x *tan(4*x)               /                                                                                                                                                                                                                                                                      \      x                        tan (4*x)                         /                                                                    \      x                        tan (4*x)                         /                                                                                                                                                                                                                                                                          \/ x *tan(4*x)                                                     x   *tan(4*x)                                                                                                       \/ x *tan(4*x)                                                                                     x   *tan(4*x)                                                                                                                                                                                                                 \/ x *tan(4*x)                                                                     \/ x *tan (4*x)                                                                 x   *tan(4*x)                                              \/ x *tan(4*x)                                              x   *tan(4*x)                                                               \/ x *tan(4*x)                                                               \/ x *tan(4*x)                                                              \/ x *tan(4*x)                                                             \/ x *tan(4*x)                                                x   *tan (4*x)                                                     \/ x *tan (4*x)                                                                                                        \/ x *tan (4*x)                                                             \/ x *tan (4*x)                                                           \/ x *tan(4*x)                                        \                                              \/ x *tan(4*x)               /     \                                              \/ x *tan(4*x)               /                               \                                              \/ x *tan(4*x)               /             \                                              \/ x *tan(4*x)               /     \                                              \/ x *tan(4*x)               /              \                                                                                                                                                                                                                x   *tan(4*x)                                                     \/ x *tan(4*x)                                                            \/ x *tan (4*x)                                                 \/ x *tan(4*x)                                            \/ x *tan(4*x)                   /     \                                                                                                                                                                                                                x   *tan(4*x)                                                     \/ x *tan(4*x)                                                            \/ x *tan (4*x)                                                 \/ x *tan(4*x)                                            \/ x *tan(4*x)                   /            \                                                                                                                                                                                                                x   *tan(4*x)                                                     \/ x *tan(4*x)                                                            \/ x *tan (4*x)                                                 \/ x *tan(4*x)                                            \/ x *tan(4*x)                   /            \  x                                /            \                                              \/ x *tan(4*x)               /                                      \                                              \/ x *tan(4*x)               /                              \                                                                                                                                                                                                                x   *tan(4*x)                                                     \/ x *tan(4*x)                                                            \/ x *tan (4*x)                                                 \/ x *tan(4*x)                                            \/ x *tan(4*x)                   /     \                                              \/ x *tan(4*x)               /                            \                                              \/ x *tan(4*x)               /                     \                                              \/ x *tan(4*x)               /       
9*cos(x) + 6*cos(2*x)*sin(x) - ------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------- + ----------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
                                                                        2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    3                                                                                          3                                                                                              3                                                                                              2                                                                                        9*x                                                                                                                                                                                                                                                                                                      27*x*sin(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 9*sin(x)                                                                                                                                                                                                                                                                                3 ___                                                                        sin(x)                                                                                               3*tan(4*x)                                                                                                                                                                                                                                                                                                               9*sin(x)*tan(4*x)                                                                                                                                                                                                                                                                                                      3*x*sin(x)                                                                                   9*x*tan(4*x)                                                                                       sin(x)*tan(4*x)                                            
                                                                    27*x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           27*sin (x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       sin (x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                3*sin (x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \/ x *tan(4*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 sin(x)
$$\frac{\frac{4 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos^{2}{\left(2 x \right)}}{3} - \frac{16 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(2 x \right)}}{3 \tan{\left(4 x \right)}} + \frac{32 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right)}{3} + \frac{4 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \sin{\left(2 x \right)}}{3} + \frac{4 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sin{\left(x \right)}} + 6 \sin{\left(x \right)} \cos{\left(2 x \right)} - \frac{8 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)} \tan{\left(4 x \right)}} + \frac{4 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4 \cdot \left(6 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)} - 36 \sin^{2}{\left(x \right)} \cos^{2}{\left(2 x \right)} + 9 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 36 \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} - 108 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)} + 27 \sin^{2}{\left(x \right)} - 54 \cos^{2}{\left(x \right)} + \frac{6 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{24 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} + \frac{9 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{2 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}}\right) \cos{\left(2 x \right)}}{9 \sin{\left(x \right)}} + 9 \cos{\left(x \right)} - \frac{4 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(2 x \right)}}{9 x} - \frac{8 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(6 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)} - 36 \sin^{2}{\left(x \right)} \cos^{2}{\left(2 x \right)} + 9 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 36 \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} - 108 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)} + 27 \sin^{2}{\left(x \right)} - 54 \cos^{2}{\left(x \right)} + \frac{6 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{24 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} + \frac{9 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{2 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}}\right)}{9 \sin{\left(x \right)} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(6 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)} - 36 \sin^{2}{\left(x \right)} \cos^{2}{\left(2 x \right)} + 9 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 36 \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} - 108 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)} + 27 \sin^{2}{\left(x \right)} - 54 \cos^{2}{\left(x \right)} + \frac{6 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{24 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} + \frac{9 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{2 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}}\right) \cos{\left(x \right)}}{3 \sin^{2}{\left(x \right)}} + \frac{8 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right)}{9 x \tan{\left(4 x \right)}} - \frac{2 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right) \cos{\left(x \right)}}{3 x \sin{\left(x \right)}} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{36 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{3}{\left(x \right)} \cos^{2}{\left(2 x \right)} - 216 \sin^{3}{\left(x \right)} \cos^{3}{\left(2 x \right)} - 36 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{3}{\left(x \right)} \sin{\left(2 x \right)} + 108 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)} + \frac{432 \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{3}{\left(x \right)} \cos^{2}{\left(2 x \right)}}{\tan{\left(4 x \right)}} - 24 \cdot \left(- 72 \tan^{2}{\left(4 x \right)} + \frac{72 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2}}{\tan^{2}{\left(4 x \right)}} - 72 + \frac{6 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x \tan{\left(4 x \right)}} + \frac{1}{x^{2}}\right) \sin^{3}{\left(x \right)} \cos{\left(2 x \right)} + 648 \sin^{3}{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(2 x \right)} - 972 \sin^{2}{\left(x \right)} \cos{\left(x \right)} \cos^{2}{\left(2 x \right)} - 27 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{3}{\left(x \right)} + 54 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{432 \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{3}{\left(x \right)} \sin{\left(2 x \right)}}{\tan{\left(4 x \right)}} + \frac{1296 \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{\tan{\left(4 x \right)}} - 36 \cdot \left(- 72 \tan^{2}{\left(4 x \right)} + \frac{72 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2}}{\tan^{2}{\left(4 x \right)}} - 72 + \frac{6 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x \tan{\left(4 x \right)}} + \frac{1}{x^{2}}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 702 \sin^{3}{\left(x \right)} \cos{\left(2 x \right)} + 972 \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(x \right)} - 972 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \cos{\left(2 x \right)} + \frac{36 \sin^{3}{\left(x \right)} \cos^{2}{\left(2 x \right)}}{x} + \frac{36 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{3}{\left(x \right)} \cos^{2}{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{324 \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{3}{\left(x \right)}}{\tan{\left(4 x \right)}} + \frac{648 \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\tan{\left(4 x \right)}} + 567 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 162 \cos^{3}{\left(x \right)} - \frac{36 \sin^{3}{\left(x \right)} \sin{\left(2 x \right)}}{x} + \frac{108 \sin^{2}{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{x} - \frac{288 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{3}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} - \frac{576 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{36 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{3}{\left(x \right)} \sin{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{108 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{24 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{3}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{27 \sin^{3}{\left(x \right)}}{x} + \frac{54 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x} + \frac{864 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan^{3}{\left(4 x \right)}} - \frac{432 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} - \frac{27 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{54 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{96 \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} + \frac{36 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(3456 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan^{2}{\left(4 x \right)} + 1728 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} + \frac{432 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)}}{x^{\frac{2}{3}}} - \frac{36 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{5}{3}}} + \frac{5 \tan{\left(4 x \right)}}{x^{\frac{8}{3}}}\right) \sin^{3}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{24 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{3}{\left(x \right)} \cos{\left(2 x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}} + \frac{96 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{3}{\left(x \right)}}{x^{\frac{4}{3}} \tan^{2}{\left(4 x \right)}} - \frac{36 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}} - \frac{8 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{3}{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}} + \frac{10 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{3}{\left(x \right)}}{x^{\frac{7}{3}} \tan{\left(4 x \right)}}}{27 \sin^{2}{\left(x \right)}} - \frac{2 \cdot \left(6 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)} - 36 \sin^{2}{\left(x \right)} \cos^{2}{\left(2 x \right)} + 9 \cdot \left(\frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{\tan{\left(4 x \right)}} + \frac{1}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 36 \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} - 108 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(2 x \right)} + 27 \sin^{2}{\left(x \right)} - 54 \cos^{2}{\left(x \right)} + \frac{6 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{24 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan^{2}{\left(4 x \right)}} + \frac{9 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} + \frac{2 \cdot \left(144 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} + \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{\frac{2}{3}}} - \frac{\tan{\left(4 x \right)}}{x^{\frac{5}{3}}}\right) \sin^{2}{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}} - \frac{2 \cdot \left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin^{2}{\left(x \right)}}{x^{\frac{4}{3}} \tan{\left(4 x \right)}}\right)}{27 x \sin{\left(x \right)}} - \frac{2 \cdot \left(6 \sin{\left(x \right)} \cos{\left(2 x \right)} + 9 \cos{\left(x \right)} - \frac{\left(12 \sqrt[3]{x} \left(\tan^{2}{\left(4 x \right)} + 1\right) + \frac{\tan{\left(4 x \right)}}{x^{\frac{2}{3}}}\right) \sin{\left(x \right)}}{\sqrt[3]{x} \tan{\left(4 x \right)}}\right)}{27 x^{2}}}{\sin{\left(x \right)}}$$
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Производная log((e^(sin(2*x))*sin(x)^(3))/(tan(4*x)*x^(1/3)))
    © Господин Экзамен – Калькулятор