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*atan(x)
-
Derivative of -((x^2+196)/x)
-
Derivative of (x-1)*e^x
-
Derivative of sqrt(x^2-6*x+13)
- Limit of the function:
-
x^3*atan(x)
-
Identical expressions
- x^ three *atan(x)
- x cubed multiply by arc tangent of gent of (x)
- x to the power of three multiply by arc tangent of gent of (x)
- x3*atan(x)
- x3*atanx
- x³*atan(x)
- x to the power of 3*atan(x)
- x^3atan(x)
- x3atan(x)
- x3atanx
- x^3atanx
-
Similar expressions
- x^3*arctan(x)
- x^3*arctanx
Derivative of x^3*atan(x)
The solution
The first derivative
[src]
3
x 2
------ + 3*x *atan(x)
2
1 + x
$$\frac{x^{3}}{x^{2} + 1} + 3 x^{2} \operatorname{atan}{\left(x \right)}$$
The second derivative
[src]
/ 3 \
| x 3*x |
2*x*|3*atan(x) - --------- + ------|
| 2 2|
| / 2\ 1 + x |
\ \1 + x / /
$$2 x \left(- \frac{x^{3}}{\left(x^{2} + 1\right)^{2}} + \frac{3 x}{x^{2} + 1} + 3 \operatorname{atan}{\left(x \right)}\right)$$
The third derivative
[src]
/ / 2 \\ | 3 | 4*x || | x *|-1 + ------|| | 3 | 2|| | 9*x 9*x \ 1 + x /| 2*|3*atan(x) - --------- + ------ + ----------------| | 2 2 2 | | / 2\ 1 + x / 2\ | \ \1 + x / \1 + x / /
$$2 \left(\frac{x^{3} \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{9 x^{3}}{\left(x^{2} + 1\right)^{2}} + \frac{9 x}{x^{2} + 1} + 3 \operatorname{atan}{\left(x \right)}\right)$$
The graph