Mister Exam

Other calculators

The derivative of the function/ arctg(x)/(x^2+1)

Derivative of arctg(x)/(x^2+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
atan(x)
-------
  2    
 x  + 1
atan⁡(x)x2+1\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1} 
atan(x)/(x^2 + 1)
The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        1           2*x*atan(x)
----------------- - -----------
/     2\ / 2    \            2 
\1 + x /*\x  + 1/    / 2    \  
                     \x  + 1/
−2xatan⁡(x)(x2+1)2+1(x2+1)(x2+1)- \frac{2 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right) \left(x^{2} + 1\right)}
Simplify
The second derivative [src] 
  //         2 \                 \
  ||      4*x  |            3*x  |
2*||-1 + ------|*atan(x) - ------|
  ||          2|                2|
  \\     1 + x /           1 + x /
----------------------------------
                    2             
            /     2\              
            \1 + x /
2(−3xx2+1+(4x2x2+1−1)atan⁡(x))(x2+1)2\frac{2 \left(- \frac{3 x}{x^{2} + 1} + \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}
Simplify
The third derivative [src] 
  /         2        /         2 \        \
  |     11*x         |      2*x  |        |
4*|-2 + ------ - 6*x*|-1 + ------|*atan(x)|
  |          2       |          2|        |
  \     1 + x        \     1 + x /        /
-------------------------------------------
                         3                 
                 /     2\                  
                 \1 + x /
4(11x2x2+1−6x(2x2x2+1−1)atan⁡(x)−2)(x2+1)3\frac{4 \left(\frac{11 x^{2}}{x^{2} + 1} - 6 x \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)} - 2\right)}{\left(x^{2} + 1\right)^{3}}
Simplify
    © Mister Exam – Calculator