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The derivative of the function/ arctan(x)/x

Derivative of arctan(x)/x

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

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from to

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The solution

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