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1/(x^2+1)
The derivative of the function/ 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
1x2+1\frac{1}{x^{2} + 1} 
1/(x^2 + 1)
Detail solution

  1. Let u=x2+1u = x^{2} + 1.

  2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

  3. Then, apply the chain rule. Multiply by ddx(x2+1)\frac{d}{d x} \left(x^{2} + 1\right):

    1. Differentiate x2+1x^{2} + 1 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant 11 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    −2x(x2+1)2- \frac{2 x}{\left(x^{2} + 1\right)^{2}}

  4. Now simplify:

    −2x(x2+1)2- \frac{2 x}{\left(x^{2} + 1\right)^{2}}

The answer is:

−2x(x2+1)2- \frac{2 x}{\left(x^{2} + 1\right)^{2}}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   -2*x  
---------
        2
/ 2    \ 
\x  + 1/
−2x(x2+1)2- \frac{2 x}{\left(x^{2} + 1\right)^{2}}
Simplify
The second derivative [src] 
  /         2 \
  |      4*x  |
2*|-1 + ------|
  |          2|
  \     1 + x /
---------------
           2   
   /     2\    
   \1 + x /
2(4x2x2+1−1)(x2+1)2\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}
Simplify
The third derivative [src] 
     /        2 \
     |     2*x  |
24*x*|1 - ------|
     |         2|
     \    1 + x /
-----------------
            3    
    /     2\     
    \1 + x /
24x(−2x2x2+1+1)(x2+1)3\frac{24 x \left(- \frac{2 x^{2}}{x^{2} + 1} + 1\right)}{\left(x^{2} + 1\right)^{3}}
Simplify
The graph
Derivative of 1/(x^2+1)
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