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The derivative of the function/ (arctg(x)/x)-ln(1+x^2)

Derivative of (arctg(x)/x)-ln(1+x^2)

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

The graph:

from to

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The solution

You have entered [src] 
atan(x)      /     2\
------- - log\1 + x /
   x
$$- \log{\left(x^{2} + 1 \right)} + \frac{\operatorname{atan}{\left(x \right)}}{x}$$ 
atan(x)/x - log(1 + x^2)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    1        atan(x)    2*x  
---------- - ------- - ------
  /     2\       2          2
x*\1 + x /      x      1 + x
$$- \frac{2 x}{x^{2} + 1} + \frac{1}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}$$
Simplify
The second derivative [src] 
  /                                                     2  \
  |    1          1       atan(x)        1           2*x   |
2*|- ------ - --------- + ------- - ----------- + ---------|
  |       2           2       3      2 /     2\           2|
  |  1 + x    /     2\       x      x *\1 + x /   /     2\ |
  \           \1 + x /                            \1 + x / /
$$2 \left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{1}{x^{2} + 1} - \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{1}{x^{2} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{3}}\right)$$
Simplify
The third derivative [src] 
  /        3                                                                  \
  |     8*x      3*atan(x)        2             3           4*x         6*x   |
2*|- --------- - --------- + ----------- + ----------- + --------- + ---------|
  |          3        4                2    3 /     2\           3           2|
  |  /     2\        x         /     2\    x *\1 + x /   /     2\    /     2\ |
  \  \1 + x /                x*\1 + x /                  \1 + x /    \1 + x / /
$$2 \left(- \frac{8 x^{3}}{\left(x^{2} + 1\right)^{3}} + \frac{6 x}{\left(x^{2} + 1\right)^{2}} + \frac{4 x}{\left(x^{2} + 1\right)^{3}} + \frac{2}{x \left(x^{2} + 1\right)^{2}} + \frac{3}{x^{3} \left(x^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(x \right)}}{x^{4}}\right)$$
Simplify
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