Производная (cot(x))^(e-x)

Вы ввели

   E - x   
cot     (x)

$$\cot^{- x + e}{\left (x \right )}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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