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Derivative of (x*arctg(x))/(1+x^2)

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

The graph:

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Piecewise:

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 graph
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 /                                         
$$\frac{2 \left(- \frac{12 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{10 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + 3 \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)\right)}{\left(x^{2} + 1\right)^{2}}$$