Производная (x-5)^cosh(x)

Вы ввели

       cosh(x)
(x - 5)       

$$\left(x - 5\right)^{\cosh{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (\cosh{\left (x \right )} \right )} + 1\right) \cosh^{\cosh{\left (x \right )}}{\left (x \right )}$

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Ответ:

$\left(\log{\left (\cosh{\left (x \right )} \right )} + 1\right) \cosh^{\cosh{\left (x \right )}}{\left (x \right )}$

Первая производная

       cosh(x) /cosh(x)                     \
(x - 5)       *|------- + log(x - 5)*sinh(x)|
               \ x - 5                      /

$$\left(x - 5\right)^{\cosh{\left (x \right )}} \left(\log{\left (x - 5 \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{x - 5}\right)$$

Вторая производная

                /                               2                                              \
        cosh(x) |/cosh(x)                      \                           cosh(x)    2*sinh(x)|
(-5 + x)       *||------- + log(-5 + x)*sinh(x)|  + cosh(x)*log(-5 + x) - --------- + ---------|
                |\ -5 + x                      /                                  2     -5 + x |
                \                                                         (-5 + x)             /

$$\left(x - 5\right)^{\cosh{\left (x \right )}} \left(\left(\log{\left (x - 5 \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{x - 5}\right)^{2} + \log{\left (x - 5 \right )} \cosh{\left (x \right )} + \frac{2 \sinh{\left (x \right )}}{x - 5} - \frac{\cosh{\left (x \right )}}{\left(x - 5\right)^{2}}\right)$$

Третья производная

                /                               3                                                                                                                                            \
        cosh(x) |/cosh(x)                      \                          3*sinh(x)   2*cosh(x)   3*cosh(x)     /cosh(x)                      \ /                       cosh(x)    2*sinh(x)\|
(-5 + x)       *||------- + log(-5 + x)*sinh(x)|  + log(-5 + x)*sinh(x) - --------- + --------- + --------- + 3*|------- + log(-5 + x)*sinh(x)|*|cosh(x)*log(-5 + x) - --------- + ---------||
                |\ -5 + x                      /                                  2           3     -5 + x      \ -5 + x                      / |                              2     -5 + x ||
                \                                                         (-5 + x)    (-5 + x)                                                  \                      (-5 + x)             //

$$\left(x - 5\right)^{\cosh{\left (x \right )}} \left(\left(\log{\left (x - 5 \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{x - 5}\right)^{3} + 3 \left(\log{\left (x - 5 \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{x - 5}\right) \left(\log{\left (x - 5 \right )} \cosh{\left (x \right )} + \frac{2 \sinh{\left (x \right )}}{x - 5} - \frac{\cosh{\left (x \right )}}{\left(x - 5\right)^{2}}\right) + \log{\left (x - 5 \right )} \sinh{\left (x \right )} + \frac{3 \cosh{\left (x \right )}}{x - 5} - \frac{3 \sinh{\left (x \right )}}{\left(x - 5\right)^{2}} + \frac{2 \cosh{\left (x \right )}}{\left(x - 5\right)^{3}}\right)$$