Derivative of arctg(x\3)

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    /x\
atan|-|
    \3/

$$\operatorname{atan}{\left(\frac{x}{3} \right)}$$

atan(x/3)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1     
----------
  /     2\
  |    x |
3*|1 + --|
  \    9 /

$$\frac{1}{3 \left(\frac{x^{2}}{9} + 1\right)}$$

Simplify

The second derivative [src]

    -2*x    
------------
           2
   /     2\ 
   |    x | 
27*|1 + --| 
   \    9 /

$$- \frac{2 x}{27 \left(\frac{x^{2}}{9} + 1\right)^{2}}$$

Simplify

The third derivative [src]

  /         2 \
  |      4*x  |
6*|-1 + ------|
  |          2|
  \     9 + x /
---------------
           2   
   /     2\    
   \9 + x /

$$\frac{6 \left(\frac{4 x^{2}}{x^{2} + 9} - 1\right)}{\left(x^{2} + 9\right)^{2}}$$

Simplify