Господин Экзамен

Другие калькуляторы

  • Как пользоваться?

  • Производная:
  • Производная 1+sin(x)
  • Производная sqrt(3*x)+2
  • Производная 3*sin(x^2)
  • Производная -((x)/(x^2+441))

  • Идентичные выражения

  • sin((шесть *x^ два)^(один / два)/log(пять *x^ два +x)^(два))
  • синус от ((6 умножить на x в квадрате ) в степени (1 делить на 2) делить на логарифм от (5 умножить на x в квадрате плюс x) в степени (2))
  • синус от ((шесть умножить на x в степени два) в степени (один делить на два) делить на логарифм от (пять умножить на x в степени два плюс x) в степени (два))
  • sin((6*x2)(1/2)/log(5*x2+x)(2))
  • sin6*x21/2/log5*x2+x2
  • sin((6*x²)^(1/2)/log(5*x²+x)^(2))
  • sin((6*x в степени 2) в степени (1/2)/log(5*x в степени 2+x) в степени (2))
  • sin((6x^2)^(1/2)/log(5x^2+x)^(2))
  • sin((6x2)(1/2)/log(5x2+x)(2))
  • sin6x21/2/log5x2+x2
  • sin6x^2^1/2/log5x^2+x^2
  • sin((6*x^2)^(1 разделить на 2) разделить на log(5*x^2+x)^(2))

  • Похожие выражения

  • sin((6*x^2)^(1/2)/log(5*x^2-x)^(2))
Производная функции/ sin((6*x^2)^(1/2)/log(5*x^2+x)^(2))

Производная sin((6*x^2)^(1/2)/log(5*x^2+x)^(2))

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

График:

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Кусочно-заданная:

Решение

Вы ввели [src] 
   /     ______   \
   |    /    2    |
   |  \/  6*x     |
sin|--------------|
   |   2/   2    \|
   \log \5*x  + x//
$$\sin{\left(\frac{\sqrt{6 x^{2}}}{\log{\left(5 x^{2} + x \right)}^{2}} \right)}$$ 
  /   /     ______   \\
  |   |    /    2    ||
d |   |  \/  6*x     ||
--|sin|--------------||
dx|   |   2/   2    \||
  \   \log \5*x  + x///
$$\frac{d}{d x} \sin{\left(\frac{\sqrt{6 x^{2}}}{\log{\left(5 x^{2} + x \right)}^{2}} \right)}$$
Преобразовать
Первая производная [src] 
                                                  /     ______   \
/     ___                 ___                \    |    /    2    |
|   \/ 6 *|x|         2*\/ 6 *|x|*(1 + 10*x) |    |  \/  6*x     |
|---------------- - -------------------------|*cos|--------------|
|     2/   2    \   /   2    \    3/   2    \|    |   2/   2    \|
\x*log \5*x  + x/   \5*x  + x/*log \5*x  + x//    \log \5*x  + x//
$$\left(- \frac{2 \sqrt{6} \left|{x}\right| \left(10 x + 1\right)}{\left(5 x^{2} + x\right) \log{\left(5 x^{2} + x \right)}^{3}} + \frac{\sqrt{6} \left|{x}\right|}{x \log{\left(5 x^{2} + x \right)}^{2}}\right) \cos{\left(\frac{\sqrt{6 x^{2}}}{\log{\left(5 x^{2} + x \right)}^{2}} \right)}$$
Упростить
Вторая производная [src] 
 /                                   2    /      ___        \         /                                                                                             2                                2                                         \    /      ___        \\ 
 |  /            2*(1 + 10*x)       \     |    \/ 6 *|x|    |     ___ |           |x|             20*|x|                2*(1 + 10*x)*sign(x)            6*(1 + 10*x) *|x|                2*(1 + 10*x) *|x|               2*(1 + 10*x)*|x|      |    |    \/ 6 *|x|    || 
 |6*|-1 + --------------------------| *sin|-----------------|   \/ 6 *|-sign(x) + --- + -------------------------- + -------------------------- - ------------------------------ - ----------------------------- + ----------------------------|*cos|-----------------|| 
 |  \     (1 + 5*x)*log(x*(1 + 5*x))/     |   2             |         |            x    (1 + 5*x)*log(x*(1 + 5*x))   (1 + 5*x)*log(x*(1 + 5*x))              2    2                           2                    x*(1 + 5*x)*log(x*(1 + 5*x))|    |   2             || 
 |                                        \log (x*(1 + 5*x))/         \                                                                           x*(1 + 5*x) *log (x*(1 + 5*x))   x*(1 + 5*x) *log(x*(1 + 5*x))                               /    \log (x*(1 + 5*x))/| 
-|----------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| 
 |                        2                                                                                                                                        x                                                                                                   | 
 \                     log (x*(1 + 5*x))                                                                                                                                                                                                                               / 
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                               2                                                                                                                                         
                                                                                                                            log (x*(1 + 5*x))
$$- \frac{\frac{6 \left(-1 + \frac{2 \cdot \left(10 x + 1\right)}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}}\right)^{2} \sin{\left(\frac{\sqrt{6} \left|{x}\right|}{\log{\left(x \left(5 x + 1\right) \right)}^{2}} \right)}}{\log{\left(x \left(5 x + 1\right) \right)}^{2}} + \frac{\sqrt{6} \left(- \operatorname{sign}{\left(x \right)} + \frac{2 \cdot \left(10 x + 1\right) \operatorname{sign}{\left(x \right)}}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{\left|{x}\right|}{x} + \frac{20 \left|{x}\right|}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{2 \cdot \left(10 x + 1\right) \left|{x}\right|}{x \left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} - \frac{2 \left(10 x + 1\right)^{2} \left|{x}\right|}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}} - \frac{6 \left(10 x + 1\right)^{2} \left|{x}\right|}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}^{2}}\right) \cos{\left(\frac{\sqrt{6} \left|{x}\right|}{\log{\left(x \left(5 x + 1\right) \right)}^{2}} \right)}}{x}}{\log{\left(x \left(5 x + 1\right) \right)}^{2}}$$
Упростить
Третья производная [src] 
  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          3        /      ___        \                                       /                                                                                             2                                2                                         \        /      ___        \\
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     ___ /            2*(1 + 10*x)       \         |    \/ 6 *|x|    |     /            2*(1 + 10*x)       \ |           |x|             20*|x|                2*(1 + 10*x)*sign(x)            6*(1 + 10*x) *|x|                2*(1 + 10*x) *|x|               2*(1 + 10*x)*|x|      |        |    \/ 6 *|x|    ||
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 3*\/ 6 *|-1 + --------------------------| *|x|*cos|-----------------|   9*|-1 + --------------------------|*|-sign(x) + --- + -------------------------- + -------------------------- - ------------------------------ - ----------------------------- + ----------------------------|*|x|*sin|-----------------||
  |      /                                                                                                                          2                                   3                                3                                                               3                              2                                                                  2                              2                                                                                              \    /      ___        \           \     (1 + 5*x)*log(x*(1 + 5*x))/         |   2             |     \     (1 + 5*x)*log(x*(1 + 5*x))/ |            x    (1 + 5*x)*log(x*(1 + 5*x))   (1 + 5*x)*log(x*(1 + 5*x))              2    2                           2                    x*(1 + 5*x)*log(x*(1 + 5*x))|        |   2             ||
  |  ___ ||x|   sign(x)           20*sign(x)                      10*|x|              2*(1 + 10*x)*DiracDelta(x)          (1 + 10*x) *|x|                  12*(1 + 10*x) *|x|                9*(1 + 10*x) *|x|              2*(1 + 10*x)*sign(x)             2*(1 + 10*x) *|x|              2*(1 + 10*x) *sign(x)              2*(1 + 10*x)*|x|                3*(1 + 10*x) *|x|              6*(1 + 10*x) *sign(x)              30*(1 + 10*x)*|x|               90*(1 + 10*x)*|x|                       |    |    \/ 6 *|x|    |                                                     \log (x*(1 + 5*x))/                                       \                                                                           x*(1 + 5*x) *log (x*(1 + 5*x))   x*(1 + 5*x) *log(x*(1 + 5*x))                               /        \log (x*(1 + 5*x))/|
2*|\/ 6 *|--- - ------- - -------------------------- - ---------------------------- - -------------------------- + ------------------------------ - ------------------------------- - ------------------------------- - ---------------------------- - ------------------------------ + ----------------------------- + ----------------------------- + ------------------------------- + ------------------------------ + ----------------------------- + ------------------------------ + DiracDelta(x)|*cos|-----------------| + --------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  |      |  2      x      (1 + 5*x)*log(x*(1 + 5*x))   x*(1 + 5*x)*log(x*(1 + 5*x))   (1 + 5*x)*log(x*(1 + 5*x))    2          2                     2          3    3                 2          3    2                x*(1 + 5*x)*log(x*(1 + 5*x))    2          3                               2                     2                               2          2    2                           2    2                           2                               2    2                             |    |   2             |                                4                                                                                                                                                          2                                                                                                                        |
  \      \ x                                                                                                       x *(1 + 5*x) *log(x*(1 + 5*x))   x *(1 + 5*x) *log (x*(1 + 5*x))   x *(1 + 5*x) *log (x*(1 + 5*x))                                  x *(1 + 5*x) *log(x*(1 + 5*x))   x*(1 + 5*x) *log(x*(1 + 5*x))   x *(1 + 5*x)*log(x*(1 + 5*x))   x *(1 + 5*x) *log (x*(1 + 5*x))   x*(1 + 5*x) *log (x*(1 + 5*x))   x*(1 + 5*x) *log(x*(1 + 5*x))   x*(1 + 5*x) *log (x*(1 + 5*x))                /    \log (x*(1 + 5*x))/                             log (x*(1 + 5*x))                                                                                                                                        x*log (x*(1 + 5*x))                                                                                                           /
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                                                                                                                                                                                                                                                                                                                                                                                                                 x*log (x*(1 + 5*x))
$$\frac{2 \cdot \left(\sqrt{6} \left(\delta\left(x\right) - \frac{2 \cdot \left(10 x + 1\right) \delta\left(x\right)}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} - \frac{\operatorname{sign}{\left(x \right)}}{x} - \frac{20 \operatorname{sign}{\left(x \right)}}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} - \frac{2 \cdot \left(10 x + 1\right) \operatorname{sign}{\left(x \right)}}{x \left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{2 \left(10 x + 1\right)^{2} \operatorname{sign}{\left(x \right)}}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}} + \frac{\left|{x}\right|}{x^{2}} - \frac{10 \left|{x}\right|}{x \left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{6 \left(10 x + 1\right)^{2} \operatorname{sign}{\left(x \right)}}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}^{2}} + \frac{30 \cdot \left(10 x + 1\right) \left|{x}\right|}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}} + \frac{2 \cdot \left(10 x + 1\right) \left|{x}\right|}{x^{2} \cdot \left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{\left(10 x + 1\right)^{2} \left|{x}\right|}{x^{2} \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}} - \frac{2 \left(10 x + 1\right)^{3} \left|{x}\right|}{x^{2} \left(5 x + 1\right)^{3} \log{\left(x \left(5 x + 1\right) \right)}} + \frac{90 \cdot \left(10 x + 1\right) \left|{x}\right|}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}^{2}} + \frac{3 \left(10 x + 1\right)^{2} \left|{x}\right|}{x^{2} \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}^{2}} - \frac{9 \left(10 x + 1\right)^{3} \left|{x}\right|}{x^{2} \left(5 x + 1\right)^{3} \log{\left(x \left(5 x + 1\right) \right)}^{2}} - \frac{12 \left(10 x + 1\right)^{3} \left|{x}\right|}{x^{2} \left(5 x + 1\right)^{3} \log{\left(x \left(5 x + 1\right) \right)}^{3}}\right) \cos{\left(\frac{\sqrt{6} \left|{x}\right|}{\log{\left(x \left(5 x + 1\right) \right)}^{2}} \right)} + \frac{3 \sqrt{6} \left(-1 + \frac{2 \cdot \left(10 x + 1\right)}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}}\right)^{3} \cos{\left(\frac{\sqrt{6} \left|{x}\right|}{\log{\left(x \left(5 x + 1\right) \right)}^{2}} \right)} \left|{x}\right|}{\log{\left(x \left(5 x + 1\right) \right)}^{4}} - \frac{9 \left(-1 + \frac{2 \cdot \left(10 x + 1\right)}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}}\right) \left(- \operatorname{sign}{\left(x \right)} + \frac{2 \cdot \left(10 x + 1\right) \operatorname{sign}{\left(x \right)}}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{\left|{x}\right|}{x} + \frac{20 \left|{x}\right|}{\left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} + \frac{2 \cdot \left(10 x + 1\right) \left|{x}\right|}{x \left(5 x + 1\right) \log{\left(x \left(5 x + 1\right) \right)}} - \frac{2 \left(10 x + 1\right)^{2} \left|{x}\right|}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}} - \frac{6 \left(10 x + 1\right)^{2} \left|{x}\right|}{x \left(5 x + 1\right)^{2} \log{\left(x \left(5 x + 1\right) \right)}^{2}}\right) \sin{\left(\frac{\sqrt{6} \left|{x}\right|}{\log{\left(x \left(5 x + 1\right) \right)}^{2}} \right)} \left|{x}\right|}{x \log{\left(x \left(5 x + 1\right) \right)}^{2}}\right)}{x \log{\left(x \left(5 x + 1\right) \right)}^{2}}$$
Упростить
    © Господин Экзамен – Калькулятор