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The derivative of the function/ x-arctg(1/x)

Derivative of x-arctg(1/x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        /1\
x - atan|-|
        \x/
$$x - \operatorname{atan}{\left(\frac{1}{x} \right)}$$ 
x - atan(1/x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
         1     
1 + -----------
     2 /    1 \
    x *|1 + --|
       |     2|
       \    x /
$$1 + \frac{1}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}$$
Simplify
The second derivative [src] 
  /          1     \
2*|-1 + -----------|
  |      2 /    1 \|
  |     x *|1 + --||
  |        |     2||
  \        \    x //
--------------------
     3 /    1 \     
    x *|1 + --|     
       |     2|     
       \    x /
$$\frac{2 \left(-1 + \frac{1}{x^{2} \left(1 + \frac{1}{x^{2}}\right)}\right)}{x^{3} \left(1 + \frac{1}{x^{2}}\right)}$$
Simplify
The third derivative [src] 
  /         7             4      \
2*|3 - ----------- + ------------|
  |     2 /    1 \              2|
  |    x *|1 + --|    4 /    1 \ |
  |       |     2|   x *|1 + --| |
  |       \    x /      |     2| |
  \                     \    x / /
----------------------------------
            4 /    1 \            
           x *|1 + --|            
              |     2|            
              \    x /
$$\frac{2 \left(3 - \frac{7}{x^{2} \left(1 + \frac{1}{x^{2}}\right)} + \frac{4}{x^{4} \left(1 + \frac{1}{x^{2}}\right)^{2}}\right)}{x^{4} \left(1 + \frac{1}{x^{2}}\right)}$$
Simplify
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