Производная cot(x)^x

Вы ввели

   x   
cot (x)

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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