Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of (x^3-1)(x^2+x+1)
-
Derivative of y/2
-
Derivative of (x+5)/(x-1)
-
Derivative of x+9
- Integral of d{x}:
- (x*arctg(x))/(1+x^2)
-
Identical expressions
- (x*arctg(x))/(one +x^ two)
- (x multiply by arctg(x)) divide by (1 plus x squared )
- (x multiply by arctg(x)) divide by (one plus x to the power of two)
- (x*arctg(x))/(1+x2)
- x*arctgx/1+x2
- (x*arctg(x))/(1+x²)
- (x*arctg(x))/(1+x to the power of 2)
- (xarctg(x))/(1+x^2)
- (xarctg(x))/(1+x2)
- xarctgx/1+x2
- xarctgx/1+x^2
- (x*arctg(x)) divide by (1+x^2)
-
Similar expressions
- (x*arctg(x))/(1-x^2)
Derivative of (x*arctg(x))/(1+x^2)
The solution
You have entered
[src]
x*atan(x)
---------
2
1 + x
$$\frac{x \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
(x*atan(x))/(1 + x^2)
The first derivative
[src]
x
------ + atan(x)
2 2
1 + x 2*x *atan(x)
---------------- - ------------
2 2
1 + x / 2\
\1 + x /
$$- \frac{2 x^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
The second derivative
[src]
/ 2 / 2 \ \
| x / x \ | 4*x | |
2*|1 - ------ - 2*x*|------ + atan(x)| + x*|-1 + ------|*atan(x)|
| 2 | 2 | | 2| |
\ 1 + x \1 + x / \ 1 + x / /
-----------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{2 \left(- \frac{x^{2}}{x^{2} + 1} - 2 x \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}$$
The third derivative
[src]
/ / 2 \ / 2 \ \
| | x | 2 | 2*x | |
| 10*x*|-1 + ------| 12*x *|-1 + ------|*atan(x)|
| / 2 \ | 2| | 2| |
| | 4*x | / x \ \ 1 + x / \ 1 + x / |
2*|3*|-1 + ------|*|------ + atan(x)| + ------------------ - ---------------------------|
| | 2| | 2 | 2 2 |
\ \ 1 + x / \1 + x / 1 + x 1 + x /
-----------------------------------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{2 \left(- \frac{12 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{10 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + 3 \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)\right)}{\left(x^{2} + 1\right)^{2}}$$