Derivative of arcctan(u/2)

You have entered [src]

    /u\
acot|-|
    \2/

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

acot(u/2)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify