Производная asin(x)^x

Вы ввели

    x   
asin (x)

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

---

Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

         /                                               3                                                  2                                                                        /                    2                        \\
         |                                            3*x               3               4*x              3*x                   2*x              /         x                        \ |     2             x                x        ||
         |                                        ----------- + ----------------- + ----------- - ------------------ + --------------------   3*|------------------- + log(asin(x))|*|----------- + ----------- + -----------------||
         |                                                5/2   /      2\                   3/2            2                   3/2              |   ________                       | |   ________           3/2   /      2\        ||
         |                                    3   /     2\      \-1 + x /*asin(x)   /     2\      /      2\            /     2\        2        |  /      2                        | |  /      2    /     2\      \-1 + x /*asin(x)||
    x    |/         x                        \    \1 - x /                          \1 - x /      \-1 + x / *asin(x)   \1 - x /   *asin (x)     \\/  1 - x  *asin(x)               / \\/  1 - x     \1 - x /                       /|
asin (x)*||------------------- + log(asin(x))|  + ----------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------|
         ||   ________                       |                                             asin(x)                                                                                   asin(x)                                        |
         ||  /      2                        |                                                                                                                                                                                      |
         \\\/  1 - x  *asin(x)               /                                                                                                                                                                                      /

$$\left(\left(\frac{x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right)^{3} + \frac{3}{\operatorname{asin}{\left (x \right )}} \left(\frac{x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right) \left(\frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left (x \right )}} + \frac{2}{\sqrt{- x^{2} + 1}}\right) + \frac{1}{\operatorname{asin}{\left (x \right )}} \left(\frac{3 x^{3}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{3 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} + \frac{4 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}} + \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}{\left (x \right )}}\right)\right) \operatorname{asin}^{x}{\left (x \right )}$$