Производная cos(x)^(log(x))

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↑ Функция f () ? - производная -го порядка

Решение

Вы ввели
[LaTeX]
   log(x)   
cos      (x)
$$\cos^{\log{\left (x \right )}}{\left (x \right )}$$
Подробное решение
[LaTeX]
  1. Не могу найти шаги в поиске этой производной.

    Но производная


Ответ:

График
[LaTeX]
Первая производная
[LaTeX]
   log(x)    /log(cos(x))   log(x)*sin(x)\
cos      (x)*|----------- - -------------|
             \     x            cos(x)   /
$$\left(- \frac{\log{\left (x \right )} \sin{\left (x \right )}}{\cos{\left (x \right )}} + \frac{1}{x} \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\log{\left (x \right )}}{\left (x \right )}$$
Вторая производная
[LaTeX]
             /                               2                             2                     \
   log(x)    |/  log(cos(x))   log(x)*sin(x)\             log(cos(x))   sin (x)*log(x)   2*sin(x)|
cos      (x)*||- ----------- + -------------|  - log(x) - ----------- - -------------- - --------|
             |\       x            cos(x)   /                   2             2          x*cos(x)|
             \                                                 x           cos (x)               /
$$\left(\left(\frac{\log{\left (x \right )} \sin{\left (x \right )}}{\cos{\left (x \right )}} - \frac{1}{x} \log{\left (\cos{\left (x \right )} \right )}\right)^{2} - \frac{\log{\left (x \right )} \sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )}} - \log{\left (x \right )} - \frac{2 \sin{\left (x \right )}}{x \cos{\left (x \right )}} - \frac{1}{x^{2}} \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\log{\left (x \right )}}{\left (x \right )}$$
Третья производная
[LaTeX]
             /                                 3                                                         /                 2                              \        2                             3                      \
   log(x)    |  /  log(cos(x))   log(x)*sin(x)\    3   2*log(cos(x))     /  log(cos(x))   log(x)*sin(x)\ |log(cos(x))   sin (x)*log(x)   2*sin(x)         |   3*sin (x)   2*log(x)*sin(x)   2*sin (x)*log(x)    3*sin(x)|
cos      (x)*|- |- ----------- + -------------|  - - + ------------- + 3*|- ----------- + -------------|*|----------- + -------------- + -------- + log(x)| - --------- - --------------- - ---------------- + ---------|
             |  \       x            cos(x)   /    x          3          \       x            cos(x)   / |      2             2          x*cos(x)         |        2           cos(x)              3            2       |
             \                                               x                                           \     x           cos (x)                        /   x*cos (x)                         cos (x)        x *cos(x)/
$$\left(- \left(\frac{\log{\left (x \right )} \sin{\left (x \right )}}{\cos{\left (x \right )}} - \frac{1}{x} \log{\left (\cos{\left (x \right )} \right )}\right)^{3} + 3 \left(\frac{\log{\left (x \right )} \sin{\left (x \right )}}{\cos{\left (x \right )}} - \frac{1}{x} \log{\left (\cos{\left (x \right )} \right )}\right) \left(\frac{\log{\left (x \right )} \sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )}} + \log{\left (x \right )} + \frac{2 \sin{\left (x \right )}}{x \cos{\left (x \right )}} + \frac{1}{x^{2}} \log{\left (\cos{\left (x \right )} \right )}\right) - \frac{2 \sin^{3}{\left (x \right )}}{\cos^{3}{\left (x \right )}} \log{\left (x \right )} - \frac{2 \log{\left (x \right )}}{\cos{\left (x \right )}} \sin{\left (x \right )} - \frac{3 \sin^{2}{\left (x \right )}}{x \cos^{2}{\left (x \right )}} - \frac{3}{x} + \frac{3 \sin{\left (x \right )}}{x^{2} \cos{\left (x \right )}} + \frac{2}{x^{3}} \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\log{\left (x \right )}}{\left (x \right )}$$