Господин Экзамен
Другие калькуляторы
- Производная неявно заданной функции
- Производная параметрической функции
- Частная производная функции
- Исследование функции по шагам
- Интеграл по шагам
- Дифференциальные уравнения по шагам
- Пределы по шагам
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Как пользоваться?
- Производная:
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Производная cos(sin(x)^(2))
- Производная 7/x^4-11*x^2
- Производная 3*t^2-e^(3*t)+1
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Производная (1/(1+(x^2)))
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Идентичные выражения
- x^(x^((sin(x))^ три))
- x в степени (x в степени (( синус от (x)) в кубе ))
- x в степени (x в степени (( синус от (x)) в степени три))
- x(x((sin(x))3))
- xxsinx3
- x^(x^((sin(x))³))
- x в степени (x в степени ((sin(x)) в степени 3))
- x^x^sinx^3
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Похожие выражения
- x^(x^((sinx)^3))
Производная x^(x^((sin(x))^3))
Решение
Вы ввели
[src]
/ 3 \ | sin (x)| \x / x
$$x^{x^{\sin^{3}{\left(x \right)}}}$$
/ / 3 \\ | | sin (x)|| d | \x /| --\x / dx
$$\frac{d}{d x} x^{x^{\sin^{3}{\left(x \right)}}}$$
Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
/ 3 \ / 3 \
| sin (x)| | sin (x) 3 / 3 \ |
\x / |x sin (x) |sin (x) 2 | |
x *|-------- + x *|------- + 3*sin (x)*cos(x)*log(x)|*log(x)|
\ x \ x / /
$$x^{x^{\sin^{3}{\left(x \right)}}} \left(x^{\sin^{3}{\left(x \right)}} \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{3}{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{x^{\sin^{3}{\left(x \right)}}}{x}\right)$$
Вторая производная
[src]
/ 3 \ / 2 /sin(x) \\
| sin (x)| 3 | 3 2 2 / 2 \ 2*sin (x)*|------ + 3*cos(x)*log(x)||
\x / sin (x) | 1 sin (x) /1 2 /sin(x) \ \ /sin(x) \ 4 |sin (x) 2 2 6*cos(x)*sin(x)| \ x /|
x *x *|- -- + x *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)| + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - |------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)*sin(x) + ------------------------------------|
| 2 \x \ x / / \ x / | 2 x | x |
\ x \ x / /
$$x^{x^{\sin^{3}{\left(x \right)}}} x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin^{4}{\left(x \right)} + x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right)^{2} - \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cdot \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)$$
Третья производная
[src]
/ / 2 \ \
| |sin (x) 2 2 6*cos(x)*sin(x)| 2 |
/ 3 \ | 3*|------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*sin(x) 2 /sin(x) \ /sin(x) \ 4 / 2 /sin(x) \\ |
| sin (x)| 3 | 3 3 / 3 3 2 2 \ 3 | 2 x | 3*sin (x)*|------ + 3*cos(x)*log(x)| 3*|------ + 3*cos(x)*log(x)| *sin (x) 3 | 2 / 2 \ 2*sin (x)*|------ + 3*cos(x)*log(x)|| / 2 \ |
\x / sin (x) |2 2*sin (x) /1 2 /sin(x) \ \ | 3 2*sin (x) 9*sin (x) 18*cos (x)*sin(x) 9*sin (x)*cos(x) 2 | /sin(x) \ 6 \ x / \ x / \ x / sin (x) /1 2 /sin(x) \ \ | 1 /sin(x) \ 4 |sin (x) 2 2 6*cos(x)*sin(x)| \ x /| 3 /sin(x) \ |sin (x) 2 2 6*cos(x)*sin(x)| |
x *x *|-- + x *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)| - |- 6*cos (x)*log(x) - --------- + --------- - ----------------- + ---------------- + 21*sin (x)*cos(x)*log(x)|*log(x) + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - -------------------------------------------------------------------------- - ------------------------------------ + ------------------------------------- + 3*x *|- + sin (x)*|------ + 3*cos(x)*log(x)|*log(x)|*|- -- + |------ + 3*cos(x)*log(x)| *sin (x)*log(x) - |------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)*sin(x) + ------------------------------------| - 3*sin (x)*|------ + 3*cos(x)*log(x)|*|------- - 6*cos (x)*log(x) + 3*sin (x)*log(x) - ---------------|*log(x)|
| 3 \x \ x / / | 3 x x 2 | \ x / x 2 x \x \ x / / | 2 \ x / | 2 x | x | \ x / | 2 x | |
\x \ x x / x \ x \ x / / \ x / /
$$x^{x^{\sin^{3}{\left(x \right)}}} x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)} \sin^{6}{\left(x \right)} - 3 \cdot \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin^{3}{\left(x \right)} + x^{2 \sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right)^{3} + \frac{3 \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{4}{\left(x \right)}}{x} + 3 x^{\sin^{3}{\left(x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)} + \frac{1}{x}\right) \left(\left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin^{4}{\left(x \right)} - \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cdot \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) - \left(21 \log{\left(x \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 6 \log{\left(x \right)} \cos^{3}{\left(x \right)} + \frac{9 \sin^{3}{\left(x \right)}}{x} - \frac{18 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{x} + \frac{9 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin^{3}{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)} - \frac{3 \cdot \left(3 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 6 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x} - \frac{3 \cdot \left(3 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right)$$
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