Производная (log(x))^x^2

Вы ввели

        / 2\
        \x /
(log(x))    

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

---

Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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