Derivative of y=arctg*(x/2)

You have entered [src]

    /x\
atan|-|
    \2/

$$\operatorname{atan}{\left(\frac{x}{2} \right)}$$

atan(x/2)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1     
----------
  /     2\
  |    x |
2*|1 + --|
  \    4 /

$$\frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}$$

Simplify

The second derivative [src]

    -x     
-----------
          2
  /     2\ 
  |    x | 
4*|1 + --| 
  \    4 /

$$- \frac{x}{4 \left(\frac{x^{2}}{4} + 1\right)^{2}}$$

Simplify

The third derivative [src]

  /         2 \
  |      4*x  |
4*|-1 + ------|
  |          2|
  \     4 + x /
---------------
           2   
   /     2\    
   \4 + x /

$$\frac{4 \left(\frac{4 x^{2}}{x^{2} + 4} - 1\right)}{\left(x^{2} + 4\right)^{2}}$$

Simplify