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 (sin(x))^(5*(e^x))
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Производная acos((x^2-4)/sqrt(x^4+16))
- Производная sin(pi)*x/x
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Производная 2*log(x+4)^3-8*x-19
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Идентичные выражения
- log(asin(log(x)))^x^ два
- логарифм от ( арксинус от ( логарифм от (x))) в степени x в квадрате
- логарифм от ( арксинус от ( логарифм от (x))) в степени x в степени два
- log(asin(log(x)))x2
- logasinlogxx2
- log(asin(log(x)))^x²
- log(asin(log(x))) в степени x в степени 2
- logasinlogx^x^2
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Похожие выражения
- log((asin(log(x)))^x^2)
- log((asin(log(x))))^(x)^2
- log(arcsin(log(x)))^x^2
Производная log(asin(log(x)))^x^2
Решение
Вы ввели
[src]
/ 2\
\x /
(log(asin(log(x))))
$$\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{x^{2}}$$
/ / 2\\ d | \x /| --\(log(asin(log(x)))) / dx
$$\frac{d}{d x} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{x^{2}}$$
Подробное решение
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Не могу найти шаги в поиске этой производной.
Но производная
Ответ:
Первая производная
[src]
/ 2\
\x / / x \
(log(asin(log(x)))) *|2*x*log(log(asin(log(x)))) + -----------------------------------------------|
| _____________ |
| / 2 |
\ \/ 1 - log (x) *asin(log(x))*log(asin(log(x)))/
$$\left(2 x \log{\left(\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \right)} + \frac{x}{\sqrt{- \log{\left(x \right)}^{2} + 1} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}}\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{x^{2}}$$
Вторая производная
[src]
/ 2\ / 2 \
\x / | 2 / 1 \ 1 1 3 log(x) |
(log(asin(log(x)))) *|2*log(log(asin(log(x)))) + x *|2*log(log(asin(log(x)))) + -----------------------------------------------| + ---------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + -----------------------------------------------|
| | _____________ | / 2 \ 2 / 2 \ 2 2 _____________ 3/2 |
| | / 2 | \-1 + log (x)/*asin (log(x))*log(asin(log(x))) \-1 + log (x)/*asin (log(x))*log (asin(log(x))) / 2 / 2 \ |
\ \ \/ 1 - log (x) *asin(log(x))*log(asin(log(x)))/ \/ 1 - log (x) *asin(log(x))*log(asin(log(x))) \1 - log (x)/ *asin(log(x))*log(asin(log(x)))/
$$\left(x^{2} \left(2 \log{\left(\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \right)} + \frac{1}{\sqrt{- \log{\left(x \right)}^{2} + 1} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}}\right)^{2} + 2 \log{\left(\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \right)} + \frac{3}{\sqrt{- \log{\left(x \right)}^{2} + 1} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} + \frac{1}{\left(\log{\left(x \right)}^{2} - 1\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}} + \frac{\log{\left(x \right)}}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} + \frac{1}{\left(\log{\left(x \right)}^{2} - 1\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{2} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}}\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{x^{2}}$$
Третья производная
[src]
/ 2 \
| 1 2 2 3*log (x) 3*log(x) 3 3*log(x) 2 3 3 3*log(x) |
| ---------------- + ---------------- + ------------------------------ + ---------------- + ---------------- + --------------------------- - ---------------------------- + ------------------------------------------------- + ------------------------------------------------ + --------------------------------------------- - ----------------------------------------------|
| 3/2 _____________ 3/2 5/2 3/2 / 2 \ 2 3/2 3/2 / 2 \ 2 |
/ 2\ | 3 / 2 \ / 2 / 2 \ 2 / 2 \ / 2 \ \-1 + log (x)/*asin(log(x)) / 2 \ / 2 \ 2 2 / 2 \ 2 \-1 + log (x)/*asin(log(x))*log(asin(log(x))) / 2 \ |
\x / | 3 / 1 \ / 1 \ / 1 1 3 log(x) \ \1 - log (x)/ \/ 1 - log (x) \1 - log (x)/ *asin (log(x)) \1 - log (x)/ \1 - log (x)/ \-1 + log (x)/ *asin(log(x)) \1 - log (x)/ *asin (log(x))*log (asin(log(x))) \1 - log (x)/ *asin (log(x))*log(asin(log(x))) \-1 + log (x)/ *asin(log(x))*log(asin(log(x)))|
(log(asin(log(x)))) *|x *|2*log(log(asin(log(x)))) + -----------------------------------------------| + 3*x*|2*log(log(asin(log(x)))) + -----------------------------------------------|*|2*log(log(asin(log(x)))) + ---------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + -----------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| | _____________ | | _____________ | | / 2 \ 2 / 2 \ 2 2 _____________ 3/2 | x*asin(log(x))*log(asin(log(x))) |
| | / 2 | | / 2 | | \-1 + log (x)/*asin (log(x))*log(asin(log(x))) \-1 + log (x)/*asin (log(x))*log (asin(log(x))) / 2 / 2 \ | |
\ \ \/ 1 - log (x) *asin(log(x))*log(asin(log(x)))/ \ \/ 1 - log (x) *asin(log(x))*log(asin(log(x)))/ \ \/ 1 - log (x) *asin(log(x))*log(asin(log(x))) \1 - log (x)/ *asin(log(x))*log(asin(log(x)))/ /
$$\left(x^{3} \left(2 \log{\left(\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \right)} + \frac{1}{\sqrt{- \log{\left(x \right)}^{2} + 1} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}}\right)^{3} + 3 x \left(2 \log{\left(\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \right)} + \frac{1}{\sqrt{- \log{\left(x \right)}^{2} + 1} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}}\right) \left(2 \log{\left(\log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \right)} + \frac{3}{\sqrt{- \log{\left(x \right)}^{2} + 1} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} + \frac{1}{\left(\log{\left(x \right)}^{2} - 1\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}} + \frac{\log{\left(x \right)}}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} + \frac{1}{\left(\log{\left(x \right)}^{2} - 1\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{2} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}}\right) + \frac{\frac{2}{\sqrt{- \log{\left(x \right)}^{2} + 1}} + \frac{3}{\left(\log{\left(x \right)}^{2} - 1\right) \operatorname{asin}{\left(\log{\left(x \right)} \right)}} - \frac{3 \log{\left(x \right)}}{\left(\log{\left(x \right)}^{2} - 1\right)^{2} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} + \frac{3 \log{\left(x \right)}}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(\log{\left(x \right)}^{2} - 1\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} - \frac{3 \log{\left(x \right)}}{\left(\log{\left(x \right)}^{2} - 1\right)^{2} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}} + \frac{1}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}}} + \frac{3 \log{\left(x \right)}^{2}}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{5}{2}}} + \frac{2}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}} + \frac{3}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}} + \frac{2}{\left(- \log{\left(x \right)}^{2} + 1\right)^{\frac{3}{2}} \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{2} \operatorname{asin}^{2}{\left(\log{\left(x \right)} \right)}}}{x \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)} \operatorname{asin}{\left(\log{\left(x \right)} \right)}}\right) \log{\left(\operatorname{asin}{\left(\log{\left(x \right)} \right)} \right)}^{x^{2}}$$
График