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(arctan(x))/(x^2+x)

Derivative of (arctan(x))/(x^2+x)

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

The graph:

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The solution

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atan(x)
-------
  2    
 x  + x
$$\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + x}$$
d /atan(x)\
--|-------|
dx|  2    |
  \ x  + x/
$$\frac{d}{d x} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + x}$$
The graph
The first derivative [src]
        1           (-1 - 2*x)*atan(x)
----------------- + ------------------
/     2\ / 2    \               2     
\1 + x /*\x  + x/       / 2    \      
                        \x  + x/      
$$\frac{\left(- 2 x - 1\right) \operatorname{atan}{\left(x \right)}}{\left(x^{2} + x\right)^{2}} + \frac{1}{\left(x^{2} + 1\right) \left(x^{2} + x\right)}$$
The second derivative [src]
   /                                  /             2\        \
   |                                  |    (1 + 2*x) |        |
   |                                  |1 - ----------|*atan(x)|
   |    1             1 + 2*x         \    x*(1 + x) /        |
-2*|--------- + ------------------- + ------------------------|
   |        2    2         /     2\           2               |
   |/     2\    x *(1 + x)*\1 + x /          x *(1 + x)       |
   \\1 + x /                                                  /
---------------------------------------------------------------
                             1 + x                             
$$- \frac{2 \left(\frac{\left(1 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \left(x + 1\right)} + \frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{2 x + 1}{x^{2} \left(x + 1\right) \left(x^{2} + 1\right)}\right)}{x + 1}$$
The third derivative [src]
  /         2                                                                                 \
  |      4*x                           /             2\               /             2\        |
  |-1 + ------                         |    (1 + 2*x) |               |    (1 + 2*x) |        |
  |          2                       3*|1 - ----------|   3*(1 + 2*x)*|2 - ----------|*atan(x)|
  |     1 + x       3*(1 + 2*x)        \    x*(1 + x) /               \    x*(1 + x) /        |
2*|----------- + ----------------- - ------------------ + ------------------------------------|
  |         2                    2             /     2\                2        2             |
  | /     2\             /     2\    x*(1 + x)*\1 + x /               x *(1 + x)              |
  \ \1 + x /     (1 + x)*\1 + x /                                                             /
-----------------------------------------------------------------------------------------------
                                           x*(1 + x)                                           
$$\frac{2 \left(\frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}} + \frac{3 \cdot \left(2 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right) \left(2 x + 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} \left(x + 1\right)^{2}} + \frac{3 \cdot \left(2 x + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)^{2}} - \frac{3 \cdot \left(1 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right)}{x \left(x + 1\right) \left(x^{2} + 1\right)}\right)}{x \left(x + 1\right)}$$
The graph
Derivative of (arctan(x))/(x^2+x)