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Derivative of:
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Integral of d{x}:
1/(2+x^2)
Limit of the function:
1/(2+x^2)
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one /(two +x^ two)
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Similar expressions
1/(2-x^2)

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

Derivative of 1/(2+x^2)

The solution

You have entered [src]

  1   
------
     2
2 + x

$$\frac{1}{x^{2} + 2}$$

1/(2 + x^2)

Detail solution

Let $u = x^{2} + 2$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 2\right)$ :
1. Differentiate $x^{2} + 2$ term by term:
  1. The derivative of the constant $2$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
The result of the chain rule is:

$- \frac{2 x}{\left(x^{2} + 2\right)^{2}}$

The answer is:

$- \frac{2 x}{\left(x^{2} + 2\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -2*x  
---------
        2
/     2\ 
\2 + x /

$$- \frac{2 x}{\left(x^{2} + 2\right)^{2}}$$

Simplify

The second derivative [src]

  /         2 \
  |      4*x  |
2*|-1 + ------|
  |          2|
  \     2 + x /
---------------
           2   
   /     2\    
   \2 + x /

$$\frac{2 \left(\frac{4 x^{2}}{x^{2} + 2} - 1\right)}{\left(x^{2} + 2\right)^{2}}$$

Simplify

The third derivative [src]

     /        2 \
     |     2*x  |
24*x*|1 - ------|
     |         2|
     \    2 + x /
-----------------
            3    
    /     2\     
    \2 + x /

$$\frac{24 x \left(- \frac{2 x^{2}}{x^{2} + 2} + 1\right)}{\left(x^{2} + 2\right)^{3}}$$

Simplify

4-я производная [src]

   /        2          4  \
   |    12*x       16*x   |
24*|1 - ------ + ---------|
   |         2           2|
   |    2 + x    /     2\ |
   \             \2 + x / /
---------------------------
                 3         
         /     2\          
         \2 + x /

$$\frac{24 \left(\frac{16 x^{4}}{\left(x^{2} + 2\right)^{2}} - \frac{12 x^{2}}{x^{2} + 2} + 1\right)}{\left(x^{2} + 2\right)^{3}}$$

Simplify

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Identical expressions

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Derivative of 1/(2+x^2)

The graph:

Piecewise:

The solution