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1/(x^2+1)

Derivative of 1/(x^2+1)

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

The graph:

from to

Piecewise:

The solution

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

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
   -2*x  
---------
        2
/ 2    \ 
\x  + 1/ 
$$- \frac{2 x}{\left(x^{2} + 1\right)^{2}}$$
The second derivative [src]
  /         2 \
  |      4*x  |
2*|-1 + ------|
  |          2|
  \     1 + x /
---------------
           2   
   /     2\    
   \1 + x /    
$$\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}$$
The third derivative [src]
     /        2 \
     |     2*x  |
24*x*|1 - ------|
     |         2|
     \    1 + x /
-----------------
            3    
    /     2\     
    \1 + x /     
$$\frac{24 x \left(- \frac{2 x^{2}}{x^{2} + 1} + 1\right)}{\left(x^{2} + 1\right)^{3}}$$
The graph
Derivative of 1/(x^2+1)