Derivative of y=arctgx/2

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acot(x)
-------
   2

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

acot(x)/2

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    x    
---------
        2
/     2\ 
\1 + x /

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

Simplify

The third derivative [src]

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

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

Simplify