Derivative of arctg(x2)

You have entered [src]

atan(x2)

$$\operatorname{atan}{\left(x_{2} \right)}$$

atan(x2)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1   
-------
      2
1 + x2

$$\frac{1}{x_{2}^{2} + 1}$$

Simplify

The second derivative [src]

  -2*x2   
----------
         2
/      2\ 
\1 + x2 /

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

Simplify

The third derivative [src]

  /          2 \
  |      4*x2  |
2*|-1 + -------|
  |           2|
  \     1 + x2 /
----------------
            2   
   /      2\    
   \1 + x2 /

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

Simplify