Производная (x+2)^sin(x)

Вы ввели

       sin(x)
(x + 2)      

$$\left(x + 2\right)^{\sin{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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