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 sqrt(1+x^2)*atan(x)
- Производная x^(5/4)
- Производная 8*cos(x)^3
- Производная (cos(7*x))^2
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Идентичные выражения
- atan(log(atan(x)))/(один +x^ два)
- арктангенс от ( логарифм от ( арктангенс от (x))) делить на (1 плюс x в квадрате )
- арктангенс от ( логарифм от ( арктангенс от (x))) делить на (один плюс x в степени два)
- atan(log(atan(x)))/(1+x2)
- atanlogatanx/1+x2
- atan(log(atan(x)))/(1+x²)
- atan(log(atan(x)))/(1+x в степени 2)
- atanlogatanx/1+x^2
- atan(log(atan(x))) разделить на (1+x^2)
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Похожие выражения
- atan(log(atan(x)))/(1-x^2)
- arctan(log(arctan(x)))/(1+x^2)
- atan(log(arctanx))/(1+x^2)
Производная atan(log(atan(x)))/(1+x^2)
Решение
Вы ввели
[src]
atan(log(atan(x)))
------------------
2
1 + x
$$\frac{\operatorname{atan}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} \right)}}{x^{2} + 1}$$
d /atan(log(atan(x)))\ --|------------------| dx| 2 | \ 1 + x /
$$\frac{d}{d x} \frac{\operatorname{atan}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} \right)}}{x^{2} + 1}$$
Первая производная
[src]
1 2*x*atan(log(atan(x)))
------------------------------------- - ----------------------
2 2
/ 2\ / 2 \ / 2\
\1 + x / *\1 + log (atan(x))/*atan(x) \1 + x /
$$- \frac{2 x \operatorname{atan}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2} \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}}$$
Вторая производная
[src]
1 2*log(atan(x))
------- + 2*x + ---------------------------
/ 2 \ atan(x) / 2 \
| 4*x | \1 + log (atan(x))/*atan(x) 4*x
2*|-1 + ------|*atan(log(atan(x))) - ------------------------------------------- - ------------------------------------
| 2| / 2\ / 2 \ / 2\ / 2 \
\ 1 + x / \1 + x /*\1 + log (atan(x))/*atan(x) \1 + x /*\1 + log (atan(x))/*atan(x)
-----------------------------------------------------------------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{2 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} \right)} - \frac{4 x}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - \frac{2 x + \frac{1}{\operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}}}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}}$$
Третья производная
[src]
/ 2 2 \
| 1 4*x 1 3*x 3*log(atan(x)) 4*log (atan(x)) 6*x*log(atan(x)) / 2 \ |
|-1 + ----------------- + ------ - ------------------------------------- + ---------------- + ------------------------------------- + -------------------------------------- + ------------------------------------ | 4*x | / 1 2*log(atan(x)) \|
| / 2\ 2 2 / 2\ / 2 \ 2 / 2\ / 2\ / 2 \ 2 2 / 2\ / 2 \ 3*|-1 + ------| 3*x*|------- + 2*x + ---------------------------||
| \1 + x /*atan (x) 1 + x \1 + x /*\1 + log (atan(x))/*atan (x) \1 + x /*atan(x) \1 + x /*\1 + log (atan(x))/*atan (x) / 2\ / 2 \ 2 \1 + x /*\1 + log (atan(x))/*atan(x) / 2 \ | 2| |atan(x) / 2 \ ||
| \1 + x /*\1 + log (atan(x))/ *atan (x) | 2*x | \ 1 + x / \ \1 + log (atan(x))/*atan(x)/|
2*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - 12*x*|-1 + ------|*atan(log(atan(x))) + --------------------------- + -------------------------------------------------|
| / 2 \ | 2| / 2 \ / 2\ / 2 \ |
\ \1 + log (atan(x))/*atan(x) \ 1 + x / \1 + log (atan(x))/*atan(x) \1 + x /*\1 + log (atan(x))/*atan(x) /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2\
\1 + x /
$$\frac{2 \left(- 12 x \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} \right)} + \frac{3 x \left(2 x + \frac{1}{\operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}}\right)}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{3 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\frac{4 x^{2}}{x^{2} + 1} - 1 + \frac{3 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{6 x \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{1}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} + \frac{3 \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} + \frac{4 \log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2}}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{1}{\left(x^{2} + 1\right) \left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}}}{\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)}^{2} + 1\right) \operatorname{atan}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{3}}$$
График