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Производная:
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Производная tan(3*x)^(4)
Производная (x^3)/(2*x+4)
Производная sqrt(1+sin(6*x)^(2))
Идентичные выражения
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( логарифм от (x) в степени четыре умножить на синус от (x)) делить на ( логарифм от (x) умножить на косинус от (x) в степени (семь)) плюс два в степени тангенс от (x) в степени (четыре)
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logx4*sinx/logx*cosx7+2tanx4
(log(x)⁴*sin(x))/(log(x)*cos(x)^(7))+2^tan(x)^(4)
(log(x)^4sin(x))/(log(x)cos(x)^(7))+2^tan(x)^(4)
(log(x)4sin(x))/(log(x)cos(x)(7))+2tan(x)(4)
logx4sinx/logxcosx7+2tanx4
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(log(x)^4*sin(x)) разделить на (log(x)*cos(x)^(7))+2^tan(x)^(4)
Похожие выражения
(log(x)^4*sin(x))/(log(x)*cos(x)^(7))-2^tan(x)^(4)
(log(x)^4*sinx)/(log(x)*cosx^(7))+2^tan(x)^(4)

Производная функции/ (log(x)^4*sin(x))/(log(x)*cos(x)^(7))+2^tan(x)^(4)

Производная (log(x)^4sin(x))/(log(x)cos(x)^(7))+2^tan(x)^(4)

Решение

Вы ввели [src]

   4                 4   
log (x)*sin(x)    tan (x)
-------------- + 2       
          7              
log(x)*cos (x)

$$\frac{\log{\left(x \right)}^{4} \sin{\left(x \right)}}{\log{\left(x \right)} \cos^{7}{\left(x \right)}} + 2^{\tan^{4}{\left(x \right)}}$$

  /   4                 4   \
d |log (x)*sin(x)    tan (x)|
--|-------------- + 2       |
dx|          7              |
  \log(x)*cos (x)           /

$$\frac{d}{d x} \left(\frac{\log{\left(x \right)}^{4} \sin{\left(x \right)}}{\log{\left(x \right)} \cos^{7}{\left(x \right)}} + 2^{\tan^{4}{\left(x \right)}}\right)$$

Преобразовать

Подробное решение

дифференцируем $2^{\tan^{4}{\left(x \right)}} + \frac{\log{\left(x \right)}^{4} \sin{\left(x \right)}}{\log{\left(x \right)} \cos^{7}{\left(x \right)}}$ почленно:
1. Применим правило производной частного:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = \log{\left(x \right)}^{4} \sin{\left(x \right)}$ и $g{\left(x \right)} = \log{\left(x \right)} \cos^{7}{\left(x \right)}$ .
  
  Чтобы найти $\frac{d}{d x} f{\left(x \right)}$ :
  1. Применяем правило производной умножения:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = \log{\left(x \right)}^{4}$ ; найдём $\frac{d}{d x} f{\left(x \right)}$ :
    1. Заменим $u = \log{\left(x \right)}$ .
    2. В силу правила, применим: $u^{4}$ получим $4 u^{3}$
    3. Затем примените цепочку правил. Умножим на $\frac{d}{d x} \log{\left(x \right)}$ :
      1. Производная $\log{\left(x \right)}$ является $\frac{1}{x}$ .
      В результате последовательности правил:
      
      $\frac{4 \log{\left(x \right)}^{3}}{x}$
    $g{\left(x \right)} = \sin{\left(x \right)}$ ; найдём $\frac{d}{d x} g{\left(x \right)}$ :
    1. Производная синуса есть косинус:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    В результате: $\log{\left(x \right)}^{4} \cos{\left(x \right)} + \frac{4 \log{\left(x \right)}^{3} \sin{\left(x \right)}}{x}$
  Чтобы найти $\frac{d}{d x} g{\left(x \right)}$ :
  1. Применяем правило производной умножения:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = \cos^{7}{\left(x \right)}$ ; найдём $\frac{d}{d x} f{\left(x \right)}$ :
    1. Заменим $u = \cos{\left(x \right)}$ .
    2. В силу правила, применим: $u^{7}$ получим $7 u^{6}$
    3. Затем примените цепочку правил. Умножим на $\frac{d}{d x} \cos{\left(x \right)}$ :
      1. Производная косинус есть минус синус:
        
        $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
      В результате последовательности правил:
      
      $- 7 \sin{\left(x \right)} \cos^{6}{\left(x \right)}$
    $g{\left(x \right)} = \log{\left(x \right)}$ ; найдём $\frac{d}{d x} g{\left(x \right)}$ :
    1. Производная $\log{\left(x \right)}$ является $\frac{1}{x}$ .
    В результате: $- 7 \log{\left(x \right)} \sin{\left(x \right)} \cos^{6}{\left(x \right)} + \frac{\cos^{7}{\left(x \right)}}{x}$
  Теперь применим правило производной деления:
  
  $\frac{\left(\log{\left(x \right)}^{4} \cos{\left(x \right)} + \frac{4 \log{\left(x \right)}^{3} \sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \cos^{7}{\left(x \right)} - \left(- 7 \log{\left(x \right)} \sin{\left(x \right)} \cos^{6}{\left(x \right)} + \frac{\cos^{7}{\left(x \right)}}{x}\right) \log{\left(x \right)}^{4} \sin{\left(x \right)}}{\log{\left(x \right)}^{2} \cos^{14}{\left(x \right)}}$
2. Заменим $u = \tan^{4}{\left(x \right)}$ .
3. $\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}$
4. Затем примените цепочку правил. Умножим на $\frac{d}{d x} \tan^{4}{\left(x \right)}$ :
  1. Заменим $u = \tan{\left(x \right)}$ .
  2. В силу правила, применим: $u^{4}$ получим $4 u^{3}$
  3. Затем примените цепочку правил. Умножим на $\frac{d}{d x} \tan{\left(x \right)}$ :
    1. Перепишем функции, чтобы дифференцировать:
      
      $\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
    2. Применим правило производной частного:
      
      $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
      
      $f{\left(x \right)} = \sin{\left(x \right)}$ и $g{\left(x \right)} = \cos{\left(x \right)}$ .
      
      Чтобы найти $\frac{d}{d x} f{\left(x \right)}$ :
      1. Производная синуса есть косинус:
        
        $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
      Чтобы найти $\frac{d}{d x} g{\left(x \right)}$ :
      1. Производная косинус есть минус синус:
        
        $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
      Теперь применим правило производной деления:
      
      $\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
    В результате последовательности правил:
    
    $\frac{4 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \tan^{3}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
  В результате последовательности правил:
  
  $\frac{4 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)} \tan^{3}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
В результате: $\frac{4 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)} \tan^{3}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\left(\log{\left(x \right)}^{4} \cos{\left(x \right)} + \frac{4 \log{\left(x \right)}^{3} \sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \cos^{7}{\left(x \right)} - \left(- 7 \log{\left(x \right)} \sin{\left(x \right)} \cos^{6}{\left(x \right)} + \frac{\cos^{7}{\left(x \right)}}{x}\right) \log{\left(x \right)}^{4} \sin{\left(x \right)}}{\log{\left(x \right)}^{2} \cos^{14}{\left(x \right)}}$
Теперь упростим:

$\frac{2^{\tan^{4}{\left(x \right)} + 2} x \log{\left(2 \right)} \cos^{6}{\left(x \right)} \tan^{3}{\left(x \right)} + \left(- 3 x \log{\left(x \right)} \cos{\left(2 x \right)} + 4 x \log{\left(x \right)} + \frac{3 \sin{\left(2 x \right)}}{2}\right) \log{\left(x \right)}^{2}}{x \cos^{8}{\left(x \right)}}$

Ответ:

$\frac{2^{\tan^{4}{\left(x \right)} + 2} x \log{\left(2 \right)} \cos^{6}{\left(x \right)} \tan^{3}{\left(x \right)} + \left(- 3 x \log{\left(x \right)} \cos{\left(2 x \right)} + 4 x \log{\left(x \right)} + \frac{3 \sin{\left(2 x \right)}}{2}\right) \log{\left(x \right)}^{2}}{x \cos^{8}{\left(x \right)}}$

График

Построить график f(x)

Построить график f'(x)

Первая производная [src]

                                                                                  /     7                             \               3          1              
                                                                             2    |  cos (x)        6                 |          4*log (x)*--------------*sin(x)
                                    4                                     log (x)*|- ------- + 7*cos (x)*log(x)*sin(x)|*sin(x)                7                 
   4          1                  tan (x)    3    /         2   \                  \     x                             /                    cos (x)*log(x)       
log (x)*--------------*cos(x) + 2       *tan (x)*\4 + 4*tan (x)/*log(2) + ---------------------------------------------------- + -------------------------------
           7                                                                                       14                                           x               
        cos (x)*log(x)                                                                          cos  (x)

$$\frac{1}{\log{\left(x \right)} \cos^{7}{\left(x \right)}} \log{\left(x \right)}^{4} \cos{\left(x \right)} + 2^{\tan^{4}{\left(x \right)}} \left(4 \tan^{2}{\left(x \right)} + 4\right) \log{\left(2 \right)} \tan^{3}{\left(x \right)} + \frac{4 \cdot \frac{1}{\log{\left(x \right)} \cos^{7}{\left(x \right)}} \log{\left(x \right)}^{3} \sin{\left(x \right)}}{x} + \frac{\left(7 \log{\left(x \right)} \sin{\left(x \right)} \cos^{6}{\left(x \right)} - \frac{\cos^{7}{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos^{14}{\left(x \right)}}$$

Упростить

Вторая производная [src]

                                                                                                              /   2                                                             \                                                                                                                                                                                                                                                                                                                            
                                                                                                         2    |cos (x)         2                  2             14*cos(x)*sin(x)|                                                                                                                                                                                                                                                                                                                            
   2    /  cos(x)                  \      3    /     1       7*sin(x)\                                log (x)*|------- - 42*sin (x)*log(x) + 7*cos (x)*log(x) + ----------------|*sin(x)                                                                                                                                     2       2    /  cos(x)                  \                                                  /  cos(x)                  \                      2    /     1       7*sin(x)\       
log (x)*|- ------ + 7*log(x)*sin(x)|   log (x)*|- -------- + --------|      3                  2              |    2                                                   x        |               2                   4                                          4                 2                                     14*log (x)*sin (x)*|- ------ + 7*log(x)*sin(x)|          4                 2                   2*|- ------ + 7*log(x)*sin(x)|*log(x)*sin(x)   4*log (x)*|- -------- + --------|*sin(x)
        \    x                     /           \  x*log(x)    cos(x) /   log (x)*sin(x)   8*log (x)           \   x                                                             /          4*log (x)*sin(x)      tan (x)    4    /       2   \              tan (x) /       2   \     2             12*log(x)*sin(x)                      \    x                     /       tan (x) /       2   \     2       6        \    x                     /                           \  x*log(x)    cos(x) /       
------------------------------------ + ------------------------------- - -------------- + --------- + ---------------------------------------------------------------------------------- - ---------------- + 8*2       *tan (x)*\1 + tan (x)/*log(2) + 12*2       *\1 + tan (x)/ *tan (x)*log(2) + ---------------- + ----------------------------------------------- + 16*2       *\1 + tan (x)/ *log (2)*tan (x) + -------------------------------------------- + ----------------------------------------
                 7                                    6                        7               6                                              9                                                2    7                                                                                                   2    7                                9                                                                                             8                                            7                   
              cos (x)                              cos (x)                  cos (x)       x*cos (x)                                        cos (x)                                            x *cos (x)                                                                                               x *cos (x)                          cos (x)                                                                                     x*cos (x)                                    x*cos (x)

$$16 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \tan^{6}{\left(x \right)} + 8 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \tan^{4}{\left(x \right)} + 12 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)} \tan^{2}{\left(x \right)} + \frac{\left(\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{3}}{\cos^{6}{\left(x \right)}} - \frac{\log{\left(x \right)}^{3} \sin{\left(x \right)}}{\cos^{7}{\left(x \right)}} + \frac{14 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\cos^{9}{\left(x \right)}} + \frac{\left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2}}{\cos^{7}{\left(x \right)}} + \frac{4 \cdot \left(\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{x \cos^{7}{\left(x \right)}} + \frac{\left(- 42 \log{\left(x \right)} \sin^{2}{\left(x \right)} + 7 \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{14 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos^{9}{\left(x \right)}} + \frac{8 \log{\left(x \right)}^{2}}{x \cos^{6}{\left(x \right)}} + \frac{2 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin{\left(x \right)}}{x \cos^{8}{\left(x \right)}} - \frac{4 \log{\left(x \right)}^{2} \sin{\left(x \right)}}{x^{2} \cos^{7}{\left(x \right)}} + \frac{12 \log{\left(x \right)} \sin{\left(x \right)}}{x^{2} \cos^{7}{\left(x \right)}}$$

Упростить

Третья производная [src]

                    /                                   2                     \                                              /   2                                                             \                                     /                             3           3            2                    2                                      \                                                                                                                                                                                                                                                                                                                                           /   2                                                             \                                                                                                                                                                                                                                                                                                                                                                                                                               /   2                                                             \                           /                                   2                     \                                                                                                   
               3    |        1           2        56*sin (x)      14*sin(x)   |                                         2    |cos (x)         2                  2             14*cos(x)*sin(x)|                                2    |         3             21*cos (x)   2*cos (x)   21*cos (x)*sin(x)   126*sin (x)*cos(x)          2                 |                                                                                                                                                                                                                                                                                                                              2       2    |cos (x)         2                  2             14*cos(x)*sin(x)|                                                                                                                                                                                                                                                                                                                                                                                                                               |cos (x)         2                  2             14*cos(x)*sin(x)|                      2    |        1           2        56*sin (x)      14*sin(x)   |                                                                                                   
            log (x)*|7 + --------- + ---------- + ---------- - ---------------|                                    2*log (x)*|------- - 42*sin (x)*log(x) + 7*cos (x)*log(x) + ----------------|                             log (x)*|- 210*sin (x)*log(x) - ---------- + --------- + ----------------- + ------------------ + 133*cos (x)*log(x)*sin(x)|*sin(x)      3    /     1       7*sin(x)\                                                    /  cos(x)                  \            /  cos(x)                  \               2    /     1       7*sin(x)\                                                                                                            28*log (x)*sin (x)*|------- - 42*sin (x)*log(x) + 7*cos (x)*log(x) + ----------------|         2    /  cos(x)                  \                                                                                                                                                                                                                                             2       3    /  cos(x)                  \        2    /     1       7*sin(x)\            /  cos(x)                  \                 4*|------- - 42*sin (x)*log(x) + 7*cos (x)*log(x) + ----------------|*log(x)*sin(x)   4*log (x)*|7 + --------- + ---------- + ---------- - ---------------|*sin(x)      /     1       7*sin(x)\                       2    /  cos(x)                  \       
     3              |     2           2    2          2        x*cos(x)*log(x)|         2           3       2                |    2                                                   x        |                                     |                           x             3               2                  x                                     |          log (x)*|- -------- + --------|*sin(x)                            2       2      2*|- ------ + 7*log(x)*sin(x)|*sin(x)   4*|- ------ + 7*log(x)*sin(x)|*log(x)   8*log (x)*|- -------- + --------|        2                    4                                          4                 3                                    |    2                                                   x        |   41*log (x)*|- ------ + 7*log(x)*sin(x)|*sin(x)         2                    4                 3                          4                 2                        2                    4                 2                           4                 3                   210*log (x)*sin (x)*|- ------ + 7*log(x)*sin(x)|   4*log (x)*|- -------- + --------|*sin(x)   2*|- ------ + 7*log(x)*sin(x)|*log(x)*sin(x)     |    2                                                   x        |                           |     2           2    2          2        x*cos(x)*log(x)|          12*|- -------- + --------|*log(x)*sin(x)   56*sin (x)*|- ------ + 7*log(x)*sin(x)|*log(x)
  log (x)           \    x *log(x)   x *log (x)    cos (x)                    /   12*log (x)   7*log (x)*sin (x)             \   x                                                             /   12*sin(x)    28*log(x)            \                                        x               x                                                         /                  \  x*log(x)    cos(x) /          32*log(x)*sin(x)   28*log (x)*sin (x)     \    x                     /            \    x                     /                    \  x*log(x)    cos(x) /   8*log (x)*sin(x)       tan (x)    5    /       2   \              tan (x) /       2   \                                     \   x                                                             /              \    x                     /          45*log (x)*sin(x)       tan (x) /       2   \     3       9          tan (x) /       2   \     3             84*sin (x)*log(x)       tan (x) /       2   \     2       7           tan (x) /       2   \     2       5                          \    x                     /             \  x*log(x)    cos(x) /            \    x                     /                   \   x                                                             /                           \    x *log(x)   x *log (x)    cos (x)                    /             \  x*log(x)    cos(x) /                            \    x                     /       
- ------- + ------------------------------------------------------------------- - ---------- - ----------------- + ----------------------------------------------------------------------------- + ---------- + ---------- - ----------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------- - ---------------- - ------------------ + ------------------------------------- + ------------------------------------- + --------------------------------- + ---------------- + 16*2       *tan (x)*\1 + tan (x)/*log(2) + 24*2       *\1 + tan (x)/ *log(2)*tan(x) + -------------------------------------------------------------------------------------- + ---------------------------------------------- + ----------------- + 64*2       *\1 + tan (x)/ *log (2)*tan (x) + 80*2       *\1 + tan (x)/ *tan (x)*log(2) + ----------------- + 96*2       *\1 + tan (x)/ *log (2)*tan (x) + 144*2       *\1 + tan (x)/ *log (2)*tan (x) + ------------------------------------------------ - ---------------------------------------- - -------------------------------------------- + ----------------------------------------------------------------------------------- + ---------------------------------------------------------------------------- + ---------------------------------------- + ----------------------------------------------
     6                                       6                                     2    6              8                                                 8                                          3    7       2    6                                                                       10                                                                                     7                          3    7              2    8                         2    8                                      7                                     6                      3    7                                                                                                                                         10                                                                   8                                   7                                                                                                        2    8                                                                                                                           10                                          2    7                                       2    8                                                                 9                                                                                 7                                                        2    7                                            9                      
  cos (x)                                 cos (x)                                 x *cos (x)        cos (x)                                           cos (x)                                      x *cos (x)   x *cos (x)                                                                 cos  (x)                                                                               cos (x)                      x *cos (x)          x *cos (x)                     x *cos (x)                              x*cos (x)                             x*cos (x)                  x *cos (x)                                                                                                                                   cos  (x)                                                             cos (x)                           x*cos (x)                                                                                                    x *cos (x)                                                                                                                     cos  (x)                                      x *cos (x)                                   x *cos (x)                                                         x*cos (x)                                                                         x*cos (x)                                                    x *cos (x)                                    x*cos (x)

$$64 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(2 \right)}^{3} \tan^{9}{\left(x \right)} + 96 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \tan^{7}{\left(x \right)} + 144 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(2 \right)}^{2} \tan^{5}{\left(x \right)} + 16 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \tan^{5}{\left(x \right)} + 80 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)} \tan^{3}{\left(x \right)} + 24 \cdot 2^{\tan^{4}{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(2 \right)} \tan{\left(x \right)} - \frac{\left(\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{3} \sin{\left(x \right)}}{\cos^{7}{\left(x \right)}} + \frac{\left(\frac{56 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 7 - \frac{14 \sin{\left(x \right)}}{x \log{\left(x \right)} \cos{\left(x \right)}} + \frac{1}{x^{2} \log{\left(x \right)}} + \frac{2}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{3}}{\cos^{6}{\left(x \right)}} - \frac{7 \log{\left(x \right)}^{3} \sin^{2}{\left(x \right)}}{\cos^{8}{\left(x \right)}} - \frac{\log{\left(x \right)}^{3}}{\cos^{6}{\left(x \right)}} + \frac{210 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2} \sin^{3}{\left(x \right)}}{\cos^{10}{\left(x \right)}} + \frac{41 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos^{8}{\left(x \right)}} + \frac{8 \cdot \left(\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{2}}{x \cos^{6}{\left(x \right)}} + \frac{4 \cdot \left(\frac{56 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 7 - \frac{14 \sin{\left(x \right)}}{x \log{\left(x \right)} \cos{\left(x \right)}} + \frac{1}{x^{2} \log{\left(x \right)}} + \frac{2}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{x \cos^{7}{\left(x \right)}} + \frac{28 \left(- 42 \log{\left(x \right)} \sin^{2}{\left(x \right)} + 7 \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{14 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{\cos^{10}{\left(x \right)}} + \frac{2 \left(- 42 \log{\left(x \right)} \sin^{2}{\left(x \right)} + 7 \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{14 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)}^{2}}{\cos^{8}{\left(x \right)}} + \frac{45 \log{\left(x \right)}^{2} \sin{\left(x \right)}}{x \cos^{7}{\left(x \right)}} - \frac{4 \cdot \left(\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{x^{2} \cos^{7}{\left(x \right)}} - \frac{\left(- 210 \log{\left(x \right)} \sin^{3}{\left(x \right)} + 133 \log{\left(x \right)} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{126 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{21 \cos^{3}{\left(x \right)}}{x} + \frac{21 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x^{2}} + \frac{2 \cos^{3}{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2} \sin{\left(x \right)}}{\cos^{10}{\left(x \right)}} + \frac{56 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)}}{x \cos^{9}{\left(x \right)}} + \frac{4 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)}}{x \cos^{7}{\left(x \right)}} + \frac{12 \cdot \left(\frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \log{\left(x \right)} \sin{\left(x \right)}}{x^{2} \cos^{7}{\left(x \right)}} - \frac{28 \log{\left(x \right)}^{2} \sin^{2}{\left(x \right)}}{x^{2} \cos^{8}{\left(x \right)}} - \frac{12 \log{\left(x \right)}^{2}}{x^{2} \cos^{6}{\left(x \right)}} + \frac{4 \left(- 42 \log{\left(x \right)} \sin^{2}{\left(x \right)} + 7 \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{14 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)}}{x \cos^{9}{\left(x \right)}} - \frac{2 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin{\left(x \right)}}{x^{2} \cos^{8}{\left(x \right)}} + \frac{84 \log{\left(x \right)} \sin^{2}{\left(x \right)}}{x^{2} \cos^{8}{\left(x \right)}} + \frac{28 \log{\left(x \right)}}{x^{2} \cos^{6}{\left(x \right)}} + \frac{8 \log{\left(x \right)}^{2} \sin{\left(x \right)}}{x^{3} \cos^{7}{\left(x \right)}} + \frac{2 \cdot \left(7 \log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{x^{2} \cos^{8}{\left(x \right)}} - \frac{32 \log{\left(x \right)} \sin{\left(x \right)}}{x^{3} \cos^{7}{\left(x \right)}} + \frac{12 \sin{\left(x \right)}}{x^{3} \cos^{7}{\left(x \right)}}$$

Упростить

График

Производная (log(x)^4*sin(x))/(log(x)*cos(x)^(7))+2^tan(x)^(4)

Другие калькуляторы

Как пользоваться?

Идентичные выражения

Похожие выражения

Производная (log(x)^4sin(x))/(log(x)cos(x)^(7))+2^tan(x)^(4)

График:

Кусочно-заданная:

Решение

Другие калькуляторы

Как пользоваться?

Идентичные выражения

Похожие выражения

Производная (log(x)^4*sin(x))/(log(x)*cos(x)^(7))+2^tan(x)^(4)

График:

Кусочно-заданная:

Решение

Производная (log(x)^4sin(x))/(log(x)cos(x)^(7))+2^tan(x)^(4)