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:
- Производная sqrt(x)+1
- Производная (sin(4*x))^2
- Производная tan(3*x-pi/4)
- Производная x^15
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Идентичные выражения
- acos(x)^(x/sin(x))
- арккосинус от (x) в степени (x делить на синус от (x))
- acos(x)(x/sin(x))
- acosxx/sinx
- acosx^x/sinx
- acos(x)^(x разделить на sin(x))
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Похожие выражения
- arccos(x)^(x/sin(x))
- arccosx^(x/sinx)
Производная acos(x)^(x/sin(x))
Решение
Вы ввели
[src]
x
------
sin(x)
(acos(x))
$$\operatorname{acos}^{\frac{x}{\sin{\left(x \right)}}}{\left(x \right)}$$
/ x \ | ------| d | sin(x)| --\(acos(x)) / dx
$$\frac{d}{d x} \operatorname{acos}^{\frac{x}{\sin{\left(x \right)}}}{\left(x \right)}$$
Подробное решение
-
Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
x
------
sin(x) // 1 x*cos(x)\ x \
(acos(x)) *||------ - --------|*log(acos(x)) - --------------------------|
||sin(x) 2 | ________ |
|\ sin (x) / / 2 |
\ \/ 1 - x *acos(x)*sin(x)/
$$\left(\left(- \frac{x \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} - \frac{x}{\sqrt{- x^{2} + 1} \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\frac{x}{\sin{\left(x \right)}}}{\left(x \right)}$$
Вторая производная
[src]
/ 2 \
|// x*cos(x)\ x \ |
|||-1 + --------|*log(acos(x)) + -------------------| |
x ||\ sin(x) / ________ | x*cos(x) |
------ || / 2 | / 2 \ -1 + -------- 2 |
sin(x) |\ \/ 1 - x *acos(x)/ | 2*cos(x) 2*x*cos (x)| 1 x sin(x) x x*cos(x) |
(acos(x)) *|----------------------------------------------------- + |x - -------- + -----------|*log(acos(x)) - ------------------- + ------------------ + ------------------- - ------------------- + --------------------------|
| sin(x) | sin(x) 2 | ________ / 2\ 2 ________ 3/2 ________ |
| \ sin (x) / / 2 \-1 + x /*acos (x) / 2 / 2\ / 2 |
\ \/ 1 - x *acos(x) \/ 1 - x *acos(x) \1 - x / *acos(x) \/ 1 - x *acos(x)*sin(x)/
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
sin(x)
$$\frac{\left(\left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{\left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{x}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right)^{2}}{\sin{\left(x \right)}} + \frac{x \cos{\left(x \right)}}{\sqrt{- x^{2} + 1} \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}} - \frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{1}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\frac{x}{\sin{\left(x \right)}}}{\left(x \right)}}{\sin{\left(x \right)}}$$
Третья производная
[src]
/ / x*cos(x) \ \
| 3 |/ 2 \ -1 + -------- 2 | |
|// x*cos(x)\ x \ / 2 \ // x*cos(x)\ x \ || 2*cos(x) 2*x*cos (x)| 1 x sin(x) x x*cos(x) | |
|||-1 + --------|*log(acos(x)) + -------------------| | 2*cos(x) 2*x*cos (x)| 3*||-1 + --------|*log(acos(x)) + -------------------|*||x - -------- + -----------|*log(acos(x)) - ------------------- + ------------------ + ------------------- - ------------------- + --------------------------| |
x ||\ sin(x) / ________ | x*cos(x) 2*|x - -------- + -----------| |\ sin(x) / ________ | || sin(x) 2 | ________ / 2\ 2 ________ 3/2 ________ | / x*cos(x)\ |
------ || / 2 | / 2 3 \ -1 + -------- | sin(x) 2 | 2 3 | / 2 | |\ sin (x) / / 2 \-1 + x /*acos (x) / 2 / 2\ / 2 | x*|-1 + --------| 2 2 |
sin(x) |\ \/ 1 - x *acos(x)/ | 6*cos (x) 5*x*cos(x) 6*x*cos (x)| 2 x sin(x) 2*x \ sin (x) / 3*x 3*x 3*x \ \/ 1 - x *acos(x)/ \ \/ 1 - x *acos(x) \/ 1 - x *acos(x) \1 - x / *acos(x) \/ 1 - x *acos(x)*sin(x)/ \ sin(x) / 2*cos(x) 2*x *cos(x) 2*x*cos (x) 2*x*cos(x) |
-(acos(x)) *|----------------------------------------------------- + |-3 - --------- + ---------- + -----------|*log(acos(x)) - ------------------ + ------------------- + ------------------ + -------------------- + ------------------------------ + ------------------- + ------------------- + ------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------- - -------------------------- - -------------------------- + --------------------------- + -------------------------|
| 2 | 2 sin(x) 3 | / 2\ 2 ________ / 2\ 2 3/2 ________ 3/2 2 5/2 sin(x) 3/2 ________ 3/2 ________ / 2\ 2 |
| sin (x) \ sin (x) sin (x) / \-1 + x /*acos (x) / 2 \-1 + x /*acos (x) / 2\ 3 / 2 / 2\ / 2\ 2 / 2\ / 2\ / 2 / 2\ / 2 2 \-1 + x /*acos (x)*sin(x)|
\ \/ 1 - x *acos(x) \1 - x / *acos (x) \/ 1 - x *acos(x) \1 - x / *acos(x) \-1 + x / *acos (x) \1 - x / *acos(x) \1 - x / *acos(x) \/ 1 - x *acos(x)*sin(x) \1 - x / *acos(x)*sin(x) \/ 1 - x *acos(x)*sin (x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
sin(x)
$$- \frac{\left(\left(\frac{5 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{6 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 - \frac{6 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{\left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{x}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right)^{3}}{\sin^{2}{\left(x \right)}} + \frac{3 \left(\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{x}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right) \left(\left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \log{\left(\operatorname{acos}{\left(x \right)} \right)} + \frac{x \cos{\left(x \right)}}{\sqrt{- x^{2} + 1} \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}} - \frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{1}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}}\right)}{\sin{\left(x \right)}} + \frac{x}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}} + \frac{2 x \cos^{2}{\left(x \right)}}{\sqrt{- x^{2} + 1} \sin^{2}{\left(x \right)} \operatorname{acos}{\left(x \right)}} + \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)}{\sqrt{- x^{2} + 1} \operatorname{acos}{\left(x \right)}} + \frac{3 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 x^{2} \cos{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}} + \frac{2 x \cos{\left(x \right)}}{\left(x^{2} - 1\right) \sin{\left(x \right)} \operatorname{acos}^{2}{\left(x \right)}} - \frac{x \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right)}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sqrt{- x^{2} + 1} \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}} + \frac{3 x^{3}}{\left(- x^{2} + 1\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} + \frac{3 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{2 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}}\right) \operatorname{acos}^{\frac{x}{\sin{\left(x \right)}}}{\left(x \right)}}{\sin{\left(x \right)}}$$
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