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The derivative of the function/ 1/2*arctg(x/2)

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

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

The graph:

from to

Piecewise:

The solution

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