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

Производная (cos(x))^tan(x)

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– производная -го порядка в точке

Примеры

График:

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Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

Решение

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

  1. Не могу найти шаги в поиске этой производной.

    Но производная

    (log⁡(tan⁡(x))+1)tan⁡tan⁡(x)(x)\left(\log{\left (\tan{\left (x \right )} \right )} + 1\right) \tan^{\tan{\left (x \right )}}{\left (x \right )}

Ответ:

(log⁡(tan⁡(x))+1)tan⁡tan⁡(x)(x)\left(\log{\left (\tan{\left (x \right )} \right )} + 1\right) \tan^{\tan{\left (x \right )}}{\left (x \right )}

График
02468-8-6-4-2-1010-2e4510e44
Первая производная [src]
   tan(x)    //       2   \               sin(x)*tan(x)\
cos      (x)*|\1 + tan (x)/*log(cos(x)) - -------------|
             \                                cos(x)   /
((tan⁡2(x)+1)log⁡(cos⁡(x))−sin⁡(x)tan⁡(x)cos⁡(x))cos⁡tan⁡(x)(x)\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} - \frac{\sin{\left (x \right )} \tan{\left (x \right )}}{\cos{\left (x \right )}}\right) \cos^{\tan{\left (x \right )}}{\left (x \right )}
Упростить
Вторая производная [src]
             /                                           2               2               /       2   \                                            \
   tan(x)    |//       2   \               sin(x)*tan(x)\             sin (x)*tan(x)   2*\1 + tan (x)/*sin(x)     /       2   \                   |
cos      (x)*||\1 + tan (x)/*log(cos(x)) - -------------|  - tan(x) - -------------- - ---------------------- + 2*\1 + tan (x)/*log(cos(x))*tan(x)|
             |\                                cos(x)   /                   2                  cos(x)                                             |
             \                                                           cos (x)                                                                  /
(((tan⁡2(x)+1)log⁡(cos⁡(x))−sin⁡(x)tan⁡(x)cos⁡(x))2+2(tan⁡2(x)+1)log⁡(cos⁡(x))tan⁡(x)−2sin⁡(x)cos⁡(x)(tan⁡2(x)+1)−sin⁡2(x)tan⁡(x)cos⁡2(x)−tan⁡(x))cos⁡tan⁡(x)(x)\left(\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} - \frac{\sin{\left (x \right )} \tan{\left (x \right )}}{\cos{\left (x \right )}}\right)^{2} + 2 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} \tan{\left (x \right )} - \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) - \frac{\sin^{2}{\left (x \right )} \tan{\left (x \right )}}{\cos^{2}{\left (x \right )}} - \tan{\left (x \right )}\right) \cos^{\tan{\left (x \right )}}{\left (x \right )}
Упростить
Третья производная [src]
             /                                                3                                                             /   2                                                    /       2   \                \                  2                    2    /       2   \                          3                                                     /       2   \              \
   tan(x)    |     //       2   \               sin(x)*tan(x)\         2        //       2   \               sin(x)*tan(x)\ |sin (x)*tan(x)     /       2   \                      2*\1 + tan (x)/*sin(x)         |     /       2   \                3*sin (x)*\1 + tan (x)/   2*sin(x)*tan(x)   2*sin (x)*tan(x)        2    /       2   \               6*\1 + tan (x)/*sin(x)*tan(x)|
cos      (x)*|-3 + |\1 + tan (x)/*log(cos(x)) - -------------|  - 3*tan (x) - 3*|\1 + tan (x)/*log(cos(x)) - -------------|*|-------------- - 2*\1 + tan (x)/*log(cos(x))*tan(x) + ---------------------- + tan(x)| + 2*\1 + tan (x)/ *log(cos(x)) - ----------------------- - --------------- - ---------------- + 4*tan (x)*\1 + tan (x)/*log(cos(x)) - -----------------------------|
             |     \                                cos(x)   /                  \                                cos(x)   / |      2                                                       cos(x)                 |                                             2                   cos(x)              3                                                             cos(x)           |
             \                                                                                                              \   cos (x)                                                                           /                                          cos (x)                                 cos (x)                                                                           /
(((tan⁡2(x)+1)log⁡(cos⁡(x))−sin⁡(x)tan⁡(x)cos⁡(x))3−3((tan⁡2(x)+1)log⁡(cos⁡(x))−sin⁡(x)tan⁡(x)cos⁡(x))(−2(tan⁡2(x)+1)log⁡(cos⁡(x))tan⁡(x)+2sin⁡(x)cos⁡(x)(tan⁡2(x)+1)+sin⁡2(x)tan⁡(x)cos⁡2(x)+tan⁡(x))+2(tan⁡2(x)+1)2log⁡(cos⁡(x))+4(tan⁡2(x)+1)log⁡(cos⁡(x))tan⁡2(x)−3sin⁡2(x)cos⁡2(x)(tan⁡2(x)+1)−6sin⁡(x)cos⁡(x)(tan⁡2(x)+1)tan⁡(x)−2sin⁡3(x)cos⁡3(x)tan⁡(x)−2sin⁡(x)cos⁡(x)tan⁡(x)−3tan⁡2(x)−3)cos⁡tan⁡(x)(x)\left(\left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} - \frac{\sin{\left (x \right )} \tan{\left (x \right )}}{\cos{\left (x \right )}}\right)^{3} - 3 \left(\left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} - \frac{\sin{\left (x \right )} \tan{\left (x \right )}}{\cos{\left (x \right )}}\right) \left(- 2 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} \tan{\left (x \right )} + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) + \frac{\sin^{2}{\left (x \right )} \tan{\left (x \right )}}{\cos^{2}{\left (x \right )}} + \tan{\left (x \right )}\right) + 2 \left(\tan^{2}{\left (x \right )} + 1\right)^{2} \log{\left (\cos{\left (x \right )} \right )} + 4 \left(\tan^{2}{\left (x \right )} + 1\right) \log{\left (\cos{\left (x \right )} \right )} \tan^{2}{\left (x \right )} - \frac{3 \sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) - \frac{6 \sin{\left (x \right )}}{\cos{\left (x \right )}} \left(\tan^{2}{\left (x \right )} + 1\right) \tan{\left (x \right )} - \frac{2 \sin^{3}{\left (x \right )}}{\cos^{3}{\left (x \right )}} \tan{\left (x \right )} - \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )}} \tan{\left (x \right )} - 3 \tan^{2}{\left (x \right )} - 3\right) \cos^{\tan{\left (x \right )}}{\left (x \right )}
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