Производная x^cot(x)^(2)

Вы ввели

    2   
 cot (x)
x       

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

---

Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

         /                                                                            2                                                                                                                                                                                                                                                                      \
    2    |                                     3                2        /       2   \                    2                                                                                        /     2                     2            /       2   \                                        \            /       2   \                2    /       2   \|
 cot (x) |  /  cot(x)     /       2   \       \     3      2*cot (x)   6*\1 + cot (x)/       /       2   \                       3    /       2   \            /  cot(x)     /       2   \       \ |  cot (x)     /       2   \           4*\1 + cot (x)/*cot(x)        2    /       2   \       |          6*\1 + cot (x)/*cot(x)   12*cot (x)*\1 + cot (x)/|
x       *|- |- ------ + 2*\1 + cot (x)/*log(x)| *cot (x) + --------- + ---------------- - 16*\1 + cot (x)/ *cot(x)*log(x) - 8*cot (x)*\1 + cot (x)/*log(x) - 3*|- ------ + 2*\1 + cot (x)/*log(x)|*|- ------- + 2*\1 + cot (x)/ *log(x) - ---------------------- + 4*cot (x)*\1 + cot (x)/*log(x)|*cot(x) + ---------------------- + ------------------------|
         |  \    x                            /                 3             x                                                                                \    x                            / |      2                                         x                                            |                     2                        x            |
         \                                                     x                                                                                                                                   \     x                                                                                       /                    x                                      /

$$x^{\cot^{2}{\left (x \right )}} \left(- \left(2 \left(\cot^{2}{\left (x \right )} + 1\right) \log{\left (x \right )} - \frac{1}{x} \cot{\left (x \right )}\right)^{3} \cot^{3}{\left (x \right )} - 3 \left(2 \left(\cot^{2}{\left (x \right )} + 1\right) \log{\left (x \right )} - \frac{1}{x} \cot{\left (x \right )}\right) \left(2 \left(\cot^{2}{\left (x \right )} + 1\right)^{2} \log{\left (x \right )} + 4 \left(\cot^{2}{\left (x \right )} + 1\right) \log{\left (x \right )} \cot^{2}{\left (x \right )} - \frac{4}{x} \left(\cot^{2}{\left (x \right )} + 1\right) \cot{\left (x \right )} - \frac{1}{x^{2}} \cot^{2}{\left (x \right )}\right) \cot{\left (x \right )} - 16 \left(\cot^{2}{\left (x \right )} + 1\right)^{2} \log{\left (x \right )} \cot{\left (x \right )} - 8 \left(\cot^{2}{\left (x \right )} + 1\right) \log{\left (x \right )} \cot^{3}{\left (x \right )} + \frac{6}{x} \left(\cot^{2}{\left (x \right )} + 1\right)^{2} + \frac{12}{x} \left(\cot^{2}{\left (x \right )} + 1\right) \cot^{2}{\left (x \right )} + \frac{6}{x^{2}} \left(\cot^{2}{\left (x \right )} + 1\right) \cot{\left (x \right )} + \frac{2}{x^{3}} \cot^{2}{\left (x \right )}\right)$$