Производная (tan(2*x))^x

Вы ввели

   x     
tan (2*x)

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

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

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

Вторая производная

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

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

Третья производная

          /                                          3                                    2                       2                                                                                                                       3                                \
          |     /    /       2     \                \                      /       2     \         /       2     \                       /    /       2     \                \ /                   /       2     \\        /       2     \                                 |
   x      |     |2*x*\1 + tan (2*x)/                |          2        12*\1 + tan (2*x)/    32*x*\1 + tan (2*x)/       /       2     \ |2*x*\1 + tan (2*x)/                | |   1             x*\1 + tan (2*x)/|   16*x*\1 + tan (2*x)/         /       2     \         |
tan (2*x)*|24 + |------------------- + log(tan(2*x))|  + 24*tan (2*x) - ------------------- - --------------------- + 12*\1 + tan (2*x)/*|------------------- + log(tan(2*x))|*|-------- + 2*x - -----------------| + --------------------- + 32*x*\1 + tan (2*x)/*tan(2*x)|
          |     \      tan(2*x)                     /                           2                    tan(2*x)                            \      tan(2*x)                     / |tan(2*x)                2         |            3                                           |
          \                                                                  tan (2*x)                                                                                         \                     tan (2*x)    /         tan (2*x)                                      /

$$\left(\frac{16 x \left(\tan^{2}{\left (2 x \right )} + 1\right)^{3}}{\tan^{3}{\left (2 x \right )}} - \frac{32 x \left(\tan^{2}{\left (2 x \right )} + 1\right)^{2}}{\tan{\left (2 x \right )}} + 32 x \left(\tan^{2}{\left (2 x \right )} + 1\right) \tan{\left (2 x \right )} + \left(\frac{2 x \left(\tan^{2}{\left (2 x \right )} + 1\right)}{\tan{\left (2 x \right )}} + \log{\left (\tan{\left (2 x \right )} \right )}\right)^{3} + 12 \left(\frac{2 x \left(\tan^{2}{\left (2 x \right )} + 1\right)}{\tan{\left (2 x \right )}} + \log{\left (\tan{\left (2 x \right )} \right )}\right) \left(\tan^{2}{\left (2 x \right )} + 1\right) \left(- \frac{x \left(\tan^{2}{\left (2 x \right )} + 1\right)}{\tan^{2}{\left (2 x \right )}} + 2 x + \frac{1}{\tan{\left (2 x \right )}}\right) - \frac{12 \left(\tan^{2}{\left (2 x \right )} + 1\right)^{2}}{\tan^{2}{\left (2 x \right )}} + 24 \tan^{2}{\left (2 x \right )} + 24\right) \tan^{x}{\left (2 x \right )}$$