Производная (1-x)^cos(x)

Вы ввели

       cos(x)
(1 - x)      

$$\left(- x + 1\right)^{\cos{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

       cos(x) /  cos(x)                    \
(1 - x)      *|- ------ - log(1 - x)*sin(x)|
              \  1 - x                     /

$$\left(- x + 1\right)^{\cos{\left (x \right )}} \left(- \log{\left (- x + 1 \right )} \sin{\left (x \right )} - \frac{\cos{\left (x \right )}}{- x + 1}\right)$$

Вторая производная

              /                            2                                           \
       cos(x) |/                    cos(x)\      cos(x)                        2*sin(x)|
(1 - x)      *||log(1 - x)*sin(x) - ------|  - --------- - cos(x)*log(1 - x) - --------|
              |\                    -1 + x/            2                        -1 + x |
              \                                (-1 + x)                                /

$$\left(- x + 1\right)^{\cos{\left (x \right )}} \left(\left(\log{\left (- x + 1 \right )} \sin{\left (x \right )} - \frac{\cos{\left (x \right )}}{x - 1}\right)^{2} - \log{\left (- x + 1 \right )} \cos{\left (x \right )} - \frac{2 \sin{\left (x \right )}}{x - 1} - \frac{\cos{\left (x \right )}}{\left(x - 1\right)^{2}}\right)$$

Третья производная

              /                              3                                                                                                                                   \
       cos(x) |  /                    cos(x)\                        3*cos(x)    2*cos(x)    3*sin(x)     /                    cos(x)\ /  cos(x)                        2*sin(x)\|
(1 - x)      *|- |log(1 - x)*sin(x) - ------|  + log(1 - x)*sin(x) - -------- + --------- + --------- + 3*|log(1 - x)*sin(x) - ------|*|--------- + cos(x)*log(1 - x) + --------||
              |  \                    -1 + x/                         -1 + x            3           2     \                    -1 + x/ |        2                        -1 + x ||
              \                                                                 (-1 + x)    (-1 + x)                                   \(-1 + x)                                //

$$\left(- x + 1\right)^{\cos{\left (x \right )}} \left(- \left(\log{\left (- x + 1 \right )} \sin{\left (x \right )} - \frac{\cos{\left (x \right )}}{x - 1}\right)^{3} + 3 \left(\log{\left (- x + 1 \right )} \sin{\left (x \right )} - \frac{\cos{\left (x \right )}}{x - 1}\right) \left(\log{\left (- x + 1 \right )} \cos{\left (x \right )} + \frac{2 \sin{\left (x \right )}}{x - 1} + \frac{\cos{\left (x \right )}}{\left(x - 1\right)^{2}}\right) + \log{\left (- x + 1 \right )} \sin{\left (x \right )} - \frac{3 \cos{\left (x \right )}}{x - 1} + \frac{3 \sin{\left (x \right )}}{\left(x - 1\right)^{2}} + \frac{2 \cos{\left (x \right )}}{\left(x - 1\right)^{3}}\right)$$