Mister Exam

Derivative of x*atan(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x*atan(x)
xatan(x)x \operatorname{atan}{\left(x \right)}
x*atan(x)
The graph
02468-8-6-4-2-1010-2020
The first derivative [src]
  x             
------ + atan(x)
     2          
1 + x           
xx2+1+atan(x)\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}
The second derivative [src]
  /       2  \
  |      x   |
2*|1 - ------|
  |         2|
  \    1 + x /
--------------
         2    
    1 + x     
2(x2x2+1+1)x2+1\frac{2 \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)}{x^{2} + 1}
The third derivative [src]
    /         2 \
    |      4*x  |
2*x*|-4 + ------|
    |          2|
    \     1 + x /
-----------------
            2    
    /     2\     
    \1 + x /     
2x(4x2x2+14)(x2+1)2\frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 4\right)}{\left(x^{2} + 1\right)^{2}}
The graph
Derivative of x*atan(x)