Производная x^cos(2*x)

Вы ввели

 cos(2*x)
x        

$$x^{\cos{\left (2 x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

          /                                  3                                                                                                                                             \
 cos(2*x) |  /  cos(2*x)                    \    12*cos(2*x)   2*cos(2*x)     /  cos(2*x)                    \ /cos(2*x)   4*sin(2*x)                    \   6*sin(2*x)                    |
x        *|- |- -------- + 2*log(x)*sin(2*x)|  - ----------- + ---------- + 3*|- -------- + 2*log(x)*sin(2*x)|*|-------- + ---------- + 4*cos(2*x)*log(x)| + ---------- + 8*log(x)*sin(2*x)|
          |  \     x                        /         x             3         \     x                        / |    2          x                         |        2                        |
          \                                                        x                                           \   x                                     /       x                         /

$$x^{\cos{\left (2 x \right )}} \left(- \left(2 \log{\left (x \right )} \sin{\left (2 x \right )} - \frac{1}{x} \cos{\left (2 x \right )}\right)^{3} + 3 \left(2 \log{\left (x \right )} \sin{\left (2 x \right )} - \frac{1}{x} \cos{\left (2 x \right )}\right) \left(4 \log{\left (x \right )} \cos{\left (2 x \right )} + \frac{4}{x} \sin{\left (2 x \right )} + \frac{1}{x^{2}} \cos{\left (2 x \right )}\right) + 8 \log{\left (x \right )} \sin{\left (2 x \right )} - \frac{12}{x} \cos{\left (2 x \right )} + \frac{6}{x^{2}} \sin{\left (2 x \right )} + \frac{2}{x^{3}} \cos{\left (2 x \right )}\right)$$