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

Производная x^sin(sin(sin(x)))

Учитель очень удивится увидев твоё верное решение производной 😼

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– производная -го порядка в точке

Примеры

График:

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Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

Виды выражений

уравнение x^sin(sin(sin(x))) = 0
неявная функция x^sin(sin(sin(x)))
производная неявной x^sin(sin(sin(x)))
канонический вид x^sin(sin(sin(x)))
система уравнений x^sin(sin(sin(x)))
интеграл x^sin(sin(sin(x)))
построить график x^sin(sin(sin(x)))
предел x^sin(sin(sin(x)))
упростить x^sin(sin(sin(x)))

Решение

Вы ввели [src]
 sin(sin(sin(x)))
x
xsin⁡(sin⁡(sin⁡(x)))x^{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}
d / sin(sin(sin(x)))\
--\x                /
dx
ddxxsin⁡(sin⁡(sin⁡(x)))\frac{d}{d x} x^{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}
Преобразовать
Подробное решение

  1. Не могу найти шаги в поиске этой производной.

    Но производная

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

Ответ:

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

График
02468-8-6-4-2-1010-1010
Построить график f(x)
Построить график f'(x)
Первая производная [src]
 sin(sin(sin(x))) /sin(sin(sin(x)))                                             \
x                *|---------------- + cos(x)*cos(sin(x))*cos(sin(sin(x)))*log(x)|
                  \       x                                                     /
xsin⁡(sin⁡(sin⁡(x)))(log⁡(x)cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))+sin⁡(sin⁡(sin⁡(x)))x)x^{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + \frac{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right)
Упростить
Вторая производная [src]
                  /                                                               2                                                                                                                                                                                                     \
 sin(sin(sin(x))) |/sin(sin(sin(x)))                                             \    sin(sin(sin(x)))      2       2                                      2                                                                                       2*cos(x)*cos(sin(x))*cos(sin(sin(x)))|
x                *||---------------- + cos(x)*cos(sin(x))*cos(sin(sin(x)))*log(x)|  - ---------------- - cos (x)*cos (sin(x))*log(x)*sin(sin(sin(x))) - cos (x)*cos(sin(sin(x)))*log(x)*sin(sin(x)) - cos(sin(x))*cos(sin(sin(x)))*log(x)*sin(x) + -------------------------------------|
                  |\       x                                                     /            2                                                                                                                                                                      x                  |
                  \                                                                          x                                                                                                                                                                                          /
xsin⁡(sin⁡(sin⁡(x)))((log⁡(x)cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))+sin⁡(sin⁡(sin⁡(x)))x)2−log⁡(x)sin⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))−log⁡(x)sin⁡(sin⁡(x))cos⁡2(x)cos⁡(sin⁡(sin⁡(x)))−log⁡(x)sin⁡(sin⁡(sin⁡(x)))cos⁡2(x)cos⁡2(sin⁡(x))+2cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))x−sin⁡(sin⁡(sin⁡(x)))x2)x^{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + \frac{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \log{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \log{\left(x \right)} \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} \cos^{2}{\left(x \right)} \cos^{2}{\left(\sin{\left(x \right)} \right)} + \frac{2 \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x} - \frac{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x^{2}}\right)
Упростить
Третья производная [src]
                  /                                                               3                                                                                                                                                                                                                                                                                                                                                                                                                                                2       2                                 2                                                                                                                                                                                                                                                                                         \
 sin(sin(sin(x))) |/sin(sin(sin(x)))                                             \      /sin(sin(sin(x)))                                             \ /sin(sin(sin(x)))      2       2                                      2                                                                                       2*cos(x)*cos(sin(x))*cos(sin(sin(x)))\   2*sin(sin(sin(x)))      3       3                                      3                                                                                       3*cos (x)*cos (sin(x))*sin(sin(sin(x)))   3*cos (x)*cos(sin(sin(x)))*sin(sin(x))   3*cos(sin(x))*cos(sin(sin(x)))*sin(x)   3*cos(x)*cos(sin(x))*cos(sin(sin(x)))        3                                                           2                                                                                                    |
x                *||---------------- + cos(x)*cos(sin(x))*cos(sin(sin(x)))*log(x)|  - 3*|---------------- + cos(x)*cos(sin(x))*cos(sin(sin(x)))*log(x)|*|---------------- + cos (x)*cos (sin(x))*log(x)*sin(sin(sin(x))) + cos (x)*cos(sin(sin(x)))*log(x)*sin(sin(x)) + cos(sin(x))*cos(sin(sin(x)))*log(x)*sin(x) - -------------------------------------| + ------------------ - cos (x)*cos (sin(x))*cos(sin(sin(x)))*log(x) - cos (x)*cos(sin(x))*cos(sin(sin(x)))*log(x) - cos(x)*cos(sin(x))*cos(sin(sin(x)))*log(x) - --------------------------------------- - -------------------------------------- - ------------------------------------- - ------------------------------------- + 3*cos (x)*cos(sin(x))*log(x)*sin(sin(x))*sin(sin(sin(x))) + 3*cos (sin(x))*cos(x)*log(x)*sin(x)*sin(sin(sin(x))) + 3*cos(x)*cos(sin(sin(x)))*log(x)*sin(x)*sin(sin(x))|
                  |\       x                                                     /      \       x                                                     / |        2                                                                                                                                                                      x                  |            3                                                                                                                                                                        x                                        x                                        x                                        2                                                                                                                                                                                          |
                  \                                                                                                                                     \       x                                                                                                                                                                                          /           x                                                                                                                                                                                                                                                                                                   x                                                                                                                                                                                           /
xsin⁡(sin⁡(sin⁡(x)))((log⁡(x)cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))+sin⁡(sin⁡(sin⁡(x)))x)3−3(log⁡(x)cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))+sin⁡(sin⁡(sin⁡(x)))x)(log⁡(x)sin⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))+log⁡(x)sin⁡(sin⁡(x))cos⁡2(x)cos⁡(sin⁡(sin⁡(x)))+log⁡(x)sin⁡(sin⁡(sin⁡(x)))cos⁡2(x)cos⁡2(sin⁡(x))−2cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))x+sin⁡(sin⁡(sin⁡(x)))x2)+3log⁡(x)sin⁡(x)sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(sin⁡(x)))+3log⁡(x)sin⁡(x)sin⁡(sin⁡(sin⁡(x)))cos⁡(x)cos⁡2(sin⁡(x))+3log⁡(x)sin⁡(sin⁡(x))sin⁡(sin⁡(sin⁡(x)))cos⁡3(x)cos⁡(sin⁡(x))−log⁡(x)cos⁡3(x)cos⁡3(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))−log⁡(x)cos⁡3(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))−log⁡(x)cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))−3sin⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))x−3sin⁡(sin⁡(x))cos⁡2(x)cos⁡(sin⁡(sin⁡(x)))x−3sin⁡(sin⁡(sin⁡(x)))cos⁡2(x)cos⁡2(sin⁡(x))x−3cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x)))x2+2sin⁡(sin⁡(sin⁡(x)))x3)x^{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + \frac{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + \frac{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + \log{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + \log{\left(x \right)} \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} \cos^{2}{\left(x \right)} \cos^{2}{\left(\sin{\left(x \right)} \right)} - \frac{2 \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x} + \frac{\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x^{2}}\right) + 3 \log{\left(x \right)} \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} + 3 \log{\left(x \right)} \sin{\left(x \right)} \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} \cos{\left(x \right)} \cos^{2}{\left(\sin{\left(x \right)} \right)} + 3 \log{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} \cos^{3}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} - \log{\left(x \right)} \cos^{3}{\left(x \right)} \cos^{3}{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \log{\left(x \right)} \cos^{3}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \log{\left(x \right)} \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \frac{3 \sin{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x} - \frac{3 \sin{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x} - \frac{3 \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} \cos^{2}{\left(x \right)} \cos^{2}{\left(\sin{\left(x \right)} \right)}}{x} - \frac{3 \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} \cos{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x^{2}} + \frac{2 \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}}{x^{3}}\right)
Упростить
График
Производная x^sin(sin(sin(x))) /media/krcore-image-pods/hash/derivative/4/ea/6ee081caa7a5c8a0a09332a5eea00.png