Производная (cot(x))^x^2

Вы ввели

        / 2\
        \x /
(cot(x))    

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

             /                                                     2                                        2                    \
        / 2\ |                   /                   /       2   \\                          2 /       2   \        /       2   \|
        \x / |                 2 |                 x*\1 + cot (x)/|       2 /       2   \   x *\1 + cot (x)/    4*x*\1 + cot (x)/|
(cot(x))    *|2*log(cot(x)) + x *|-2*log(cot(x)) + ---------------|  + 2*x *\1 + cot (x)/ - ----------------- - -----------------|
             |                   \                      cot(x)    /                                 2                 cot(x)     |
             \                                                                                   cot (x)                         /

$$\left(x^{2} \left(\frac{x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} - 2 \log{\left (\cot{\left (x \right )} \right )}\right)^{2} - \frac{x^{2} \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot^{2}{\left (x \right )}} + 2 x^{2} \left(\cot^{2}{\left (x \right )} + 1\right) - \frac{4 x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} + 2 \log{\left (\cot{\left (x \right )} \right )}\right) \cot^{x^{2}}{\left (x \right )}$$

Третья производная

             /                                       3                   /                                              2                                         \                                          /                                                      2                    \\
        / 2\ |     /                   /       2   \\                    |                               2 /       2   \       2 /       2   \       /       2   \|       /                   /       2   \\ |                                       2 /       2   \        /       2   \||
        \x / |   3 |                 x*\1 + cot (x)/|      /       2   \ |         3         2          x *\1 + cot (x)/    2*x *\1 + cot (x)/   3*x*\1 + cot (x)/|       |                 x*\1 + cot (x)/| |                    2 /       2   \   x *\1 + cot (x)/    4*x*\1 + cot (x)/||
(cot(x))    *|- x *|-2*log(cot(x)) + ---------------|  - 2*\1 + cot (x)/*|-6*x + ------ + 2*x *cot(x) + ----------------- - ------------------ + -----------------| + 3*x*|-2*log(cot(x)) + ---------------|*|-2*log(cot(x)) - 2*x *\1 + cot (x)/ + ----------------- + -----------------||
             |     \                      cot(x)    /                    |       cot(x)                         3                 cot(x)                 2        |       \                      cot(x)    / |                                              2                 cot(x)     ||
             \                                                           \                                   cot (x)                                  cot (x)     /                                          \                                           cot (x)                         //

$$\left(- x^{3} \left(\frac{x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} - 2 \log{\left (\cot{\left (x \right )} \right )}\right)^{3} + 3 x \left(\frac{x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} - 2 \log{\left (\cot{\left (x \right )} \right )}\right) \left(\frac{x^{2} \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot^{2}{\left (x \right )}} - 2 x^{2} \left(\cot^{2}{\left (x \right )} + 1\right) + \frac{4 x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} - 2 \log{\left (\cot{\left (x \right )} \right )}\right) - 2 \left(\cot^{2}{\left (x \right )} + 1\right) \left(\frac{x^{2} \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot^{3}{\left (x \right )}} - \frac{2 x^{2} \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} + 2 x^{2} \cot{\left (x \right )} + \frac{3 x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot^{2}{\left (x \right )}} - 6 x + \frac{3}{\cot{\left (x \right )}}\right)\right) \cot^{x^{2}}{\left (x \right )}$$