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

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -x   
------
 2    
x  + 1
$$\frac{\left(-1\right) x}{x^{2} + 1}$$ 
(-x)/(x^2 + 1)
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                 2  
    1         2*x   
- ------ + ---------
   2               2
  x  + 1   / 2    \ 
           \x  + 1/
$$\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{1}{x^{2} + 1}$$
Simplify
The second derivative [src] 
    /        2 \
    |     4*x  |
2*x*|3 - ------|
    |         2|
    \    1 + x /
----------------
           2    
   /     2\     
   \1 + x /
$$\frac{2 x \left(- \frac{4 x^{2}}{x^{2} + 1} + 3\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
The third derivative [src] 
  /                  /         2 \\
  |                2 |      2*x  ||
  |             4*x *|-1 + ------||
  |        2         |          2||
  |     4*x          \     1 + x /|
6*|1 - ------ + ------------------|
  |         2              2      |
  \    1 + x          1 + x       /
-----------------------------------
                     2             
             /     2\              
             \1 + x /
$$\frac{6 \left(\frac{4 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{4 x^{2}}{x^{2} + 1} + 1\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
The graph
Derivative of (-x)/(x^2+1)
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