Производная (4*x)^cos(x)

Вы ввели

     cos(x)
(4*x)      

$$\left(4 x\right)^{\cos{\left (x \right )}}$$

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)                  \
(4*x)      *|------ - log(4*x)*sin(x)|
            \  x                     /

$$\left(4 x\right)^{\cos{\left (x \right )}} \left(- \log{\left (4 x \right )} \sin{\left (x \right )} + \frac{1}{x} \cos{\left (x \right )}\right)$$

Вторая производная

            /                          2                                      \
     cos(x) |/                  cos(x)\    cos(x)                     2*sin(x)|
(4*x)      *||log(4*x)*sin(x) - ------|  - ------ - cos(x)*log(4*x) - --------|
            |\                    x   /       2                          x    |
            \                                x                                /

$$\left(4 x\right)^{\cos{\left (x \right )}} \left(\left(\log{\left (4 x \right )} \sin{\left (x \right )} - \frac{1}{x} \cos{\left (x \right )}\right)^{2} - \log{\left (4 x \right )} \cos{\left (x \right )} - \frac{2}{x} \sin{\left (x \right )} - \frac{1}{x^{2}} \cos{\left (x \right )}\right)$$

Третья производная

            /                            3                                                                                                                        \
     cos(x) |  /                  cos(x)\                      3*cos(x)   2*cos(x)   3*sin(x)     /                  cos(x)\ /cos(x)                     2*sin(x)\|
(4*x)      *|- |log(4*x)*sin(x) - ------|  + log(4*x)*sin(x) - -------- + -------- + -------- + 3*|log(4*x)*sin(x) - ------|*|------ + cos(x)*log(4*x) + --------||
            |  \                    x   /                         x           3          2        \                    x   / |   2                          x    ||
            \                                                                x          x                                    \  x                                //

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