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
-
Как пользоваться?
- Производная:
-
Производная e^x*cot(x)
-
Производная log(log(tan(x)/log(5)))/log(16)
- Производная x*e^(-1)
- Производная sqrt((x^2)+4*x+20)
-
Идентичные выражения
- atan(atan(x))/asin(asin(x))
- арктангенс от ( арктангенс от (x)) делить на арксинус от ( арксинус от (x))
- atanatanx/asinasinx
- atan(atan(x)) разделить на asin(asin(x))
-
Похожие выражения
- arctan(arctan(x))/arcsin(arcsin(x))
- atan(arctanx)/asin(arcsinx)
Производная atan(atan(x))/asin(asin(x))
Решение
Вы ввели
[src]
atan(atan(x)) ------------- asin(asin(x))
$$\frac{\operatorname{atan}{\left(\operatorname{atan}{\left(x \right)} \right)}}{\operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}}$$
d /atan(atan(x))\ --|-------------| dx\asin(asin(x))/
$$\frac{d}{d x} \frac{\operatorname{atan}{\left(\operatorname{atan}{\left(x \right)} \right)}}{\operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}}$$
Первая производная
[src]
1 atan(atan(x))
------------------------------------- - --------------------------------------------
/ 2\ / 2 \ ________ ______________
\1 + x /*\1 + atan (x)/*asin(asin(x)) / 2 / 2 2
\/ 1 - x *\/ 1 - asin (x) *asin (asin(x))
$$\frac{1}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} - \frac{\operatorname{atan}{\left(\operatorname{atan}{\left(x \right)} \right)}}{\sqrt{- x^{2} + 1} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1} \operatorname{asin}^{2}{\left(\operatorname{asin}{\left(x \right)} \right)}}$$
Вторая производная
[src]
/ asin(x) x 2 \
|--------------------------- - ----------------------------- + ---------------------------------------|*atan(atan(x)) / atan(x) \
| 3/2 3/2 ______________ / 2\ / 2 \ | 2*|x + ------------|
|/ 2 \ / 2\ / 2\ / 2 \-1 + x /*\-1 + asin (x)/*asin(asin(x))| | 2 |
\\1 - asin (x)/ *\-1 + x / \1 - x / *\/ 1 - asin (x) / \ 1 + atan (x)/ 2
--------------------------------------------------------------------------------------------------------------------- - ------------------------ - -------------------------------------------------------------------
asin(asin(x)) 2 ________ ______________
/ 2\ / 2 \ / 2\ / 2 \ / 2 / 2
\1 + x / *\1 + atan (x)/ \1 + x /*\1 + atan (x)/*\/ 1 - x *\/ 1 - asin (x) *asin(asin(x))
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
asin(asin(x))
$$\frac{\frac{\left(- \frac{x}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1}} + \frac{2}{\left(x^{2} - 1\right) \left(\operatorname{asin}^{2}{\left(x \right)} - 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(- \operatorname{asin}^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \left(x^{2} - 1\right)}\right) \operatorname{atan}{\left(\operatorname{atan}{\left(x \right)} \right)}}{\operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} - \frac{2 \left(x + \frac{\operatorname{atan}{\left(x \right)}}{\operatorname{atan}^{2}{\left(x \right)} + 1}\right)}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} - \frac{2}{\sqrt{- x^{2} + 1} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1} \left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}}}{\operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}}$$
Третья производная
[src]
/ 2 2 \ / 2 2 \
| 1 1 3*x 3*asin (x) 6 6*asin(x) 3*x*asin(x) 6*x | | 1 4*x 4*atan (x) 6*x*atan(x) | / asin(x) x 2 \
|----------------------------- + ----------------------------- + ----------------------------- + ----------------------------- + -------------------------------------------- - ------------------------------------------ + ---------------------------- + ----------------------------------------|*atan(atan(x)) 2*|-1 - ----------------------- + ------ + ------------------------ + -----------------------| 3*|--------------------------- - ----------------------------- + ---------------------------------------| / atan(x) \
| 3/2 3/2 3/2 ______________ 5/2 ______________ 3/2 5/2 3/2 3/2 3/2 2 3/2 2 2 | | / 2\ / 2 \ 2 2 / 2\ / 2 \| | 3/2 3/2 ______________ / 2\ / 2 \ | 6*|x + ------------|
|/ 2\ / 2 \ / 2\ / 2 / 2\ / 2 / 2\ / 2 \ / 2\ / 2 \ 2 / 2\ / 2 \ / 2 \ / 2\ / 2\ / 2 \ | | \1 + x /*\1 + atan (x)/ 1 + x / 2\ / 2 \ \1 + x /*\1 + atan (x)/| |/ 2 \ / 2\ / 2\ / 2 \-1 + x /*\-1 + asin (x)/*asin(asin(x))| | 2 |
\\1 - x / *\1 - asin (x)/ \1 - x / *\/ 1 - asin (x) \1 - x / *\/ 1 - asin (x) \1 - x / *\1 - asin (x)/ \1 - x / *\1 - asin (x)/ *asin (asin(x)) \1 - x / *\-1 + asin (x)/ *asin(asin(x)) \1 - asin (x)/ *\-1 + x / \-1 + x / *\-1 + asin (x)/*asin(asin(x))/ \ \1 + x /*\1 + atan (x)/ / \\1 - asin (x)/ *\-1 + x / \1 - x / *\/ 1 - asin (x) / \ 1 + atan (x)/
- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------
asin(asin(x)) 2 / 2\ / 2 \ 2 ________ ______________
/ 2\ / 2 \ \1 + x /*\1 + atan (x)/*asin(asin(x)) / 2\ / 2 \ / 2 / 2
\1 + x / *\1 + atan (x)/ \1 + x / *\1 + atan (x)/*\/ 1 - x *\/ 1 - asin (x) *asin(asin(x))
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
asin(asin(x))
$$\frac{- \frac{\left(\frac{6 x}{\left(x^{2} - 1\right)^{2} \left(\operatorname{asin}^{2}{\left(x \right)} - 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} + \frac{3 x \operatorname{asin}{\left(x \right)}}{\left(- \operatorname{asin}^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \left(x^{2} - 1\right)^{2}} + \frac{3 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1}} + \frac{1}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1}} - \frac{6 \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(\operatorname{asin}^{2}{\left(x \right)} - 1\right)^{2} \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} + \frac{1}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(- \operatorname{asin}^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}}} + \frac{3 \operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(- \operatorname{asin}^{2}{\left(x \right)} + 1\right)^{\frac{5}{2}}} + \frac{6}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(- \operatorname{asin}^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(\operatorname{asin}{\left(x \right)} \right)}}\right) \operatorname{atan}{\left(\operatorname{atan}{\left(x \right)} \right)}}{\operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} + \frac{3 \left(- \frac{x}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1}} + \frac{2}{\left(x^{2} - 1\right) \left(\operatorname{asin}^{2}{\left(x \right)} - 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(- \operatorname{asin}^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}} \left(x^{2} - 1\right)}\right)}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}} + \frac{2 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} + \frac{6 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} - 1 + \frac{4 \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)^{2}} - \frac{1}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}\right)}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} + \frac{6 \left(x + \frac{\operatorname{atan}{\left(x \right)}}{\operatorname{atan}^{2}{\left(x \right)} + 1}\right)}{\sqrt{- x^{2} + 1} \sqrt{- \operatorname{asin}^{2}{\left(x \right)} + 1} \left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}}}{\operatorname{asin}{\left(\operatorname{asin}{\left(x \right)} \right)}}$$
График