Mister Exam

Other calculators

The derivative of the function/ xarctgx^3

Derivative of xarctgx^3

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
      3   
x*atan (x)
$$x \operatorname{atan}^{3}{\left(x \right)}$$ 
x*atan(x)^3
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                   2   
    3      3*x*atan (x)
atan (x) + ------------
                   2   
              1 + x
$$\frac{3 x \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \operatorname{atan}^{3}{\left(x \right)}$$
Simplify
The second derivative [src] 
  /  x*(-1 + x*atan(x))          \        
6*|- ------------------ + atan(x)|*atan(x)
  |             2                |        
  \        1 + x                 /        
------------------------------------------
                       2                  
                  1 + x
$$\frac{6 \left(- \frac{x \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
Simplify
The third derivative [src] 
  /  /                                     2     2   \                             \
  |  |  1          2      6*x*atan(x)   4*x *atan (x)|                             |
6*|x*|------ - atan (x) - ----------- + -------------| - 3*(-1 + x*atan(x))*atan(x)|
  |  |     2                      2              2   |                             |
  \  \1 + x                  1 + x          1 + x    /                             /
------------------------------------------------------------------------------------
                                             2                                      
                                     /     2\                                       
                                     \1 + x /
$$\frac{6 \left(x \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) - 3 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
    © Mister Exam – Calculator