Производная tan(x)^(2*x)

Вы ввели

   2*x   
tan   (x)

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

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Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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