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1/(1+x^2)^2

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

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

The graph:

from to

Piecewise:

The solution

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

  2. Apply the power rule: goes to

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

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. Apply the power rule: goes to

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
       -4*x       
------------------
                 2
/     2\ /     2\ 
\1 + x /*\1 + x / 
$$- \frac{4 x}{\left(x^{2} + 1\right) \left(x^{2} + 1\right)^{2}}$$
The second derivative [src]
  /         2 \
  |      6*x  |
4*|-1 + ------|
  |          2|
  \     1 + x /
---------------
           3   
   /     2\    
   \1 + x /    
$$\frac{4 \left(\frac{6 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{3}}$$
The third derivative [src]
     /        2 \
     |     8*x  |
24*x*|3 - ------|
     |         2|
     \    1 + x /
-----------------
            4    
    /     2\     
    \1 + x /     
$$\frac{24 x \left(- \frac{8 x^{2}}{x^{2} + 1} + 3\right)}{\left(x^{2} + 1\right)^{4}}$$
The graph
Derivative of 1/(1+x^2)^2