Производная (asin(x))^cosh(x)

Вы ввели

    cosh(x)   
asin       (x)

$$\operatorname{asin}^{\cosh{\left (x \right )}}{\left (x \right )}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

---

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)      \
asin       (x)*|log(asin(x))*sinh(x) + -------------------|
               |                          ________        |
               |                         /      2         |
               \                       \/  1 - x  *asin(x)/

$$\left(\log{\left (\operatorname{asin}{\left (x \right )} \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}}\right) \operatorname{asin}^{\cosh{\left (x \right )}}{\left (x \right )}$$

Вторая производная

               /                                            2                                                                                        \
    cosh(x)    |/                             cosh(x)      \                                cosh(x)              2*sinh(x)             x*cosh(x)     |
asin       (x)*||log(asin(x))*sinh(x) + -------------------|  + cosh(x)*log(asin(x)) + ------------------ + ------------------- + -------------------|
               ||                          ________        |                           /      2\     2         ________                   3/2        |
               ||                         /      2         |                           \-1 + x /*asin (x)     /      2            /     2\           |
               \\                       \/  1 - x  *asin(x)/                                                \/  1 - x  *asin(x)   \1 - x /   *asin(x)/

$$\left(\frac{x \cosh{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left (x \right )}} + \left(\log{\left (\operatorname{asin}{\left (x \right )} \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}}\right)^{2} + \log{\left (\operatorname{asin}{\left (x \right )} \right )} \cosh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left (x \right )}} + \frac{2 \sinh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}}\right) \operatorname{asin}^{\cosh{\left (x \right )}}{\left (x \right )}$$

Третья производная

               /                                            3                                                                                                                                                                                                                                                                                                              2           \
    cosh(x)    |/                             cosh(x)      \                             /                             cosh(x)      \ /                            cosh(x)              2*sinh(x)             x*cosh(x)     \         cosh(x)              2*cosh(x)              3*cosh(x)            3*sinh(x)            3*x*cosh(x)           3*x*sinh(x)           3*x *cosh(x)   |
asin       (x)*||log(asin(x))*sinh(x) + -------------------|  + log(asin(x))*sinh(x) + 3*|log(asin(x))*sinh(x) + -------------------|*|cosh(x)*log(asin(x)) + ------------------ + ------------------- + -------------------| + ------------------- + -------------------- + ------------------- + ------------------ - ------------------- + ------------------- + -------------------|
               ||                          ________        |                             |                          ________        | |                       /      2\     2         ________                   3/2        |           3/2                   3/2               ________           /      2\     2               2                    3/2                   5/2        |
               ||                         /      2         |                             |                         /      2         | |                       \-1 + x /*asin (x)     /      2            /     2\           |   /     2\              /     2\        3        /      2            \-1 + x /*asin (x)   /      2\      2      /     2\              /     2\           |
               \\                       \/  1 - x  *asin(x)/                             \                       \/  1 - x  *asin(x)/ \                                            \/  1 - x  *asin(x)   \1 - x /   *asin(x)/   \1 - x /   *asin(x)   \1 - x /   *asin (x)   \/  1 - x  *asin(x)                        \-1 + x / *asin (x)   \1 - x /   *asin(x)   \1 - x /   *asin(x)/

$$\left(\frac{3 x^{2} \cosh{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}} \operatorname{asin}{\left (x \right )}} - \frac{3 x \cosh{\left (x \right )}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left (x \right )}} + \frac{3 x \sinh{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left (x \right )}} + \left(\log{\left (\operatorname{asin}{\left (x \right )} \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}}\right)^{3} + 3 \left(\log{\left (\operatorname{asin}{\left (x \right )} \right )} \sinh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}}\right) \left(\frac{x \cosh{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left (x \right )}} + \log{\left (\operatorname{asin}{\left (x \right )} \right )} \cosh{\left (x \right )} + \frac{\cosh{\left (x \right )}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left (x \right )}} + \frac{2 \sinh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}}\right) + \log{\left (\operatorname{asin}{\left (x \right )} \right )} \sinh{\left (x \right )} + \frac{3 \sinh{\left (x \right )}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left (x \right )}} + \frac{3 \cosh{\left (x \right )}}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + \frac{\cosh{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left (x \right )}} + \frac{2 \cosh{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left (x \right )}}\right) \operatorname{asin}^{\cosh{\left (x \right )}}{\left (x \right )}$$