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

Производная tan(x)^log(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]
   log(x)   
tan      (x)
$$\tan^{\log{\left (x \right )}}{\left (x \right )}$$
Подробное решение

  1. Не могу найти шаги в поиске этой производной.

    Но производная

Ответ:

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