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1/(x^2-1)
Graphing y =:
1/(x^2-1)
Integral of d{x}:
1/(x^2-1)
Identical expressions
one /(x^ two - one)
1 divide by (x squared minus 1)
one divide by (x to the power of two minus one)
1/(x2-1)
1/x2-1
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Similar expressions
1/(x^2)-1
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

The graph

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Derivative of 1/(x^2-1)

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Piecewise:

The solution