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x*arctgx
The derivative of the function/ x*arctgx

Derivative of x*arctgx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x*acot(x)
$$x \operatorname{acot}{\left(x \right)}$$ 
x*acot(x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    x             
- ------ + acot(x)
       2          
  1 + x
$$- \frac{x}{x^{2} + 1} + \operatorname{acot}{\left(x \right)}$$
Simplify
The second derivative [src] 
  /        2  \
  |       x   |
2*|-1 + ------|
  |          2|
  \     1 + x /
---------------
          2    
     1 + x
$$\frac{2 \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1}$$
Simplify
The third derivative [src] 
    /        2 \
    |     4*x  |
2*x*|4 - ------|
    |         2|
    \    1 + x /
----------------
           2    
   /     2\     
   \1 + x /
$$\frac{2 x \left(- \frac{4 x^{2}}{x^{2} + 1} + 4\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
The graph
Derivative of x*arctgx
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