Производная cot(x)^(6*x)

Вы ввели

   6*x   
cot   (x)

$$\cot^{6 x}{\left (x \right )}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(6 x\right)^{6 x} \left(\log{\left (6 x \right )} + 1\right)$

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Ответ:

$\left(6 x\right)^{6 x} \left(\log{\left (6 x \right )} + 1\right)$

Первая производная

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

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

Вторая производная

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

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

Третья производная

            /                                       3                              2                                               3                    2                                                                                      \
            |       /                 /       2   \\                  /       2   \                                   /       2   \        /       2   \                     /                 /       2   \\ /                  /       2   \\|
     6*x    |       |               x*\1 + cot (x)/|         2      3*\1 + cot (x)/        /       2   \          2*x*\1 + cot (x)/    4*x*\1 + cot (x)/       /       2   \ |               x*\1 + cot (x)/| |         2      x*\1 + cot (x)/||
6*cot   (x)*|6 - 36*|-log(cot(x)) + ---------------|  + 6*cot (x) - ---------------- - 4*x*\1 + cot (x)/*cot(x) - ------------------ + ------------------ + 18*\1 + cot (x)/*|-log(cot(x)) + ---------------|*|-2*x + ------ + ---------------||
            |       \                    cot(x)    /                       2                                              3                  cot(x)                          \                    cot(x)    / |       cot(x)          2       ||
            \                                                           cot (x)                                        cot (x)                                                                                \                    cot (x)    //

$$6 \left(- \frac{2 x \left(\cot^{2}{\left (x \right )} + 1\right)^{3}}{\cot^{3}{\left (x \right )}} + \frac{4 x \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot{\left (x \right )}} - 4 x \left(\cot^{2}{\left (x \right )} + 1\right) \cot{\left (x \right )} - 36 \left(\frac{x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} - \log{\left (\cot{\left (x \right )} \right )}\right)^{3} + 18 \left(\frac{x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot{\left (x \right )}} - \log{\left (\cot{\left (x \right )} \right )}\right) \left(\cot^{2}{\left (x \right )} + 1\right) \left(\frac{x \left(\cot^{2}{\left (x \right )} + 1\right)}{\cot^{2}{\left (x \right )}} - 2 x + \frac{2}{\cot{\left (x \right )}}\right) - \frac{3 \left(\cot^{2}{\left (x \right )} + 1\right)^{2}}{\cot^{2}{\left (x \right )}} + 6 \cot^{2}{\left (x \right )} + 6\right) \cot^{6 x}{\left (x \right )}$$