Производная (asin(x))^(log(x))

Вы ввели

    log(x)   
asin      (x)

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

---

Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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