Производная функции/ От одной переменной/ y' = (sin(x)^(tan(x)))'

Производная sin(x)^(tan(x))

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– производная -го порядка в точке

Примеры

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Кусочно-заданная:

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Решение

Вы ввели [src]
   tan(x)   
sin      (x)
$$\sin^{\tan{\left (x \right )}}{\left (x \right )}$$
Подробное решение

  1. Не могу найти шаги в поиске этой производной.

    Но производная

Ответ:

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Первая производная [src]
   tan(x)    //       2   \               cos(x)*tan(x)\
sin      (x)*|\1 + tan (x)/*log(sin(x)) + -------------|
             \                                sin(x)   /
$$\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} + \frac{\cos{\left (x \right )} \tan{\left (x \right )}}{\sin{\left (x \right )}}\right) \sin^{\tan{\left (x \right )}}{\left (x \right )}$$
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Вторая производная [src]
             /                                           2               2               /       2   \                                            \
   tan(x)    |//       2   \               cos(x)*tan(x)\             cos (x)*tan(x)   2*\1 + tan (x)/*cos(x)     /       2   \                   |
sin      (x)*||\1 + tan (x)/*log(sin(x)) + -------------|  - tan(x) - -------------- + ---------------------- + 2*\1 + tan (x)/*log(sin(x))*tan(x)|
             |\                                sin(x)   /                   2                  sin(x)                                             |
             \                                                           sin (x)                                                                  /
$$\left(\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} + \frac{\cos{\left (x \right )} \tan{\left (x \right )}}{\sin{\left (x \right )}}\right)^{2} + 2 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} \tan{\left (x \right )} + \frac{2 \cos{\left (x \right )}}{\sin{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) - \tan{\left (x \right )} - \frac{\cos^{2}{\left (x \right )} \tan{\left (x \right )}}{\sin^{2}{\left (x \right )}}\right) \sin^{\tan{\left (x \right )}}{\left (x \right )}$$
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Третья производная [src]
             /                                                3                              2                                                             /             2               /       2   \                                            \        2    /       2   \        3                                                                       /       2   \              \
   tan(x)    |     //       2   \               cos(x)*tan(x)\         2        /       2   \                  //       2   \               cos(x)*tan(x)\ |          cos (x)*tan(x)   2*\1 + tan (x)/*cos(x)     /       2   \                   |   3*cos (x)*\1 + tan (x)/   2*cos (x)*tan(x)   2*cos(x)*tan(x)        2    /       2   \               6*\1 + tan (x)/*cos(x)*tan(x)|
sin      (x)*|-3 + |\1 + tan (x)/*log(sin(x)) + -------------|  - 3*tan (x) + 2*\1 + tan (x)/ *log(sin(x)) + 3*|\1 + tan (x)/*log(sin(x)) + -------------|*|-tan(x) - -------------- + ---------------------- + 2*\1 + tan (x)/*log(sin(x))*tan(x)| - ----------------------- + ---------------- + --------------- + 4*tan (x)*\1 + tan (x)/*log(sin(x)) + -----------------------------|
             |     \                                sin(x)   /                                                 \                                sin(x)   / |                2                  sin(x)                                             |              2                     3                sin(x)                                                         sin(x)           |
             \                                                                                                                                             \             sin (x)                                                                  /           sin (x)               sin (x)                                                                                             /
$$\left(\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} + \frac{\cos{\left (x \right )} \tan{\left (x \right )}}{\sin{\left (x \right )}}\right)^{3} + 3 \left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} + \frac{\cos{\left (x \right )} \tan{\left (x \right )}}{\sin{\left (x \right )}}\right) \left(2 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} \tan{\left (x \right )} + \frac{2 \cos{\left (x \right )}}{\sin{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) - \tan{\left (x \right )} - \frac{\cos^{2}{\left (x \right )} \tan{\left (x \right )}}{\sin^{2}{\left (x \right )}}\right) + 2 \left(\tan^{2}{\left (x \right )} + 1\right)^{2} \log{\left (\sin{\left (x \right )} \right )} + 4 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\sin{\left (x \right )} \right )} \tan^{2}{\left (x \right )} + \frac{6 \cos{\left (x \right )}}{\sin{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) \tan{\left (x \right )} - \frac{3 \cos^{2}{\left (x \right )}}{\sin^{2}{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) - 3 \tan^{2}{\left (x \right )} - 3 + \frac{2 \cos{\left (x \right )}}{\sin{\left (x \right )}} \tan{\left (x \right )} + \frac{2 \cos^{3}{\left (x \right )}}{\sin^{3}{\left (x \right )}} \tan{\left (x \right )}\right) \sin^{\tan{\left (x \right )}}{\left (x \right )}$$
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