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Graphing y =:
1/(x^2+1)
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1/(x^2+1)
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Similar expressions
y=(x+1)*(1-(1/((x^2)+1)))*(1+(1/(1+(cosx)^2)))
1/(x^2-1)

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

Derivative of 1/(x^2+1)

The solution

You have entered [src]

  1   
------
 2    
x  + 1

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

1/(x^2 + 1)

Detail solution

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

$- \frac{2 x}{\left(x^{2} + 1\right)^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

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Derivative of 1/(x^2+1)

The graph:

Piecewise:

The solution