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 e^x*cot(x)
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Производная log(log(tan(x)/log(5)))/log(16)
- Производная x*e^(-1)
- Производная sqrt((x^2)+4*x+20)
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Идентичные выражения
- (x*cos(x))^(log(x*cos(x)))
- (x умножить на косинус от (x)) в степени ( логарифм от (x умножить на косинус от (x)))
- (x*cos(x))(log(x*cos(x)))
- x*cosxlogx*cosx
- (xcos(x))^(log(xcos(x)))
- (xcos(x))(log(xcos(x)))
- xcosxlogxcosx
- xcosx^logxcosx
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Похожие выражения
- (x*cosx)^(log(x*cosx))
Производная (x*cos(x))^(log(x*cos(x)))
Решение
Вы ввели
[src]
log(x*cos(x)) (x*cos(x))
$$\left(x \cos{\left(x \right)}\right)^{\log{\left(x \cos{\left(x \right)} \right)}}$$
d / log(x*cos(x))\ --\(x*cos(x)) / dx
$$\frac{d}{d x} \left(x \cos{\left(x \right)}\right)^{\log{\left(x \cos{\left(x \right)} \right)}}$$
Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
log(x*cos(x))
2*(x*cos(x)) *(-x*sin(x) + cos(x))*log(x*cos(x))
------------------------------------------------------------
x*cos(x)
$$\frac{2 \left(x \cos{\left(x \right)}\right)^{\log{\left(x \cos{\left(x \right)} \right)}} \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)}}{x \cos{\left(x \right)}}$$
Вторая производная
[src]
/ 2 2 2 \
log(x*cos(x)) | (-cos(x) + x*sin(x)) (-cos(x) + x*sin(x))*log(x*cos(x)) (-cos(x) + x*sin(x))*log(x*cos(x))*sin(x) 2*(-cos(x) + x*sin(x)) *log (x*cos(x))|
2*(x*cos(x)) *|-(2*sin(x) + x*cos(x))*log(x*cos(x)) + --------------------- + ---------------------------------- - ----------------------------------------- + --------------------------------------|
\ x*cos(x) x cos(x) x*cos(x) /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x*cos(x)
$$\frac{2 \left(x \cos{\left(x \right)}\right)^{\log{\left(x \cos{\left(x \right)} \right)}} \left(- \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} - \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \log{\left(x \cos{\left(x \right)} \right)}^{2}}{x \cos{\left(x \right)}} + \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)}}{x} + \frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x \cos{\left(x \right)}}\right)}{x \cos{\left(x \right)}}$$
Третья производная
[src]
/ 2 2 2 3 3 3 2 2 2 2 2 \
log(x*cos(x)) | 3*(-cos(x) + x*sin(x)) 2*(-cos(x) + x*sin(x))*log(x*cos(x)) 2*(2*sin(x) + x*cos(x))*log(x*cos(x)) 6*(-cos(x) + x*sin(x)) *log (x*cos(x)) 6*(-cos(x) + x*sin(x)) *log(x*cos(x)) 4*(-cos(x) + x*sin(x)) *log (x*cos(x)) 2*(2*sin(x) + x*cos(x))*log(x*cos(x))*sin(x) 2*sin (x)*(-cos(x) + x*sin(x))*log(x*cos(x)) 3*(-cos(x) + x*sin(x)) *sin(x) 3*(-cos(x) + x*sin(x))*(2*sin(x) + x*cos(x)) 2*(-cos(x) + x*sin(x))*log(x*cos(x))*sin(x) 6*(-cos(x) + x*sin(x)) *log (x*cos(x))*sin(x) 6*log (x*cos(x))*(-cos(x) + x*sin(x))*(2*sin(x) + x*cos(x))|
2*(x*cos(x)) *|(-3*cos(x) + x*sin(x))*log(x*cos(x)) - (-cos(x) + x*sin(x))*log(x*cos(x)) - ----------------------- - ------------------------------------ + ------------------------------------- - -------------------------------------- - ------------------------------------- - -------------------------------------- - -------------------------------------------- - -------------------------------------------- + ------------------------------ + -------------------------------------------- + ------------------------------------------- + --------------------------------------------- + -----------------------------------------------------------|
| 2 2 x 2 2 2 2 2 cos(x) 2 2 x*cos(x) x*cos(x) 2 x*cos(x) |
\ x *cos(x) x x *cos(x) x *cos (x) x *cos (x) cos (x) x*cos (x) x*cos (x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x*cos(x)
$$\frac{2 \left(x \cos{\left(x \right)}\right)^{\log{\left(x \cos{\left(x \right)} \right)}} \left(\left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} - \frac{2 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \log{\left(x \cos{\left(x \right)} \right)}^{2} \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)}} + \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)}^{2}}{x \cos{\left(x \right)}} - \frac{4 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{3} \log{\left(x \cos{\left(x \right)} \right)}^{3}}{x^{2} \cos^{2}{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)} \sin{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)}}{x} - \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \log{\left(x \cos{\left(x \right)} \right)}^{2}}{x^{2} \cos{\left(x \right)}} + \frac{3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)}} + \frac{3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x \cos{\left(x \right)}} - \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{3} \log{\left(x \cos{\left(x \right)} \right)}}{x^{2} \cos^{2}{\left(x \right)}} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \cos{\left(x \right)} \right)}}{x^{2}} - \frac{3 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{x^{2} \cos{\left(x \right)}}\right)}{x \cos{\left(x \right)}}$$
График