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Integral of d{x}:
2/(x^2-1)
Graphing y =:
2/(x^2-1)
How do you in partial fractions?:
2/(x^2-1)
Identical expressions
two /(x^ two - one)
2 divide by (x squared minus 1)
two divide by (x to the power of two minus one)
2/(x2-1)
2/x2-1
2/(x²-1)
2/(x to the power of 2-1)
2/x^2-1
2 divide by (x^2-1)
Similar expressions
2/(x^2+1)

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

Derivative of 2/(x^2-1)

The solution

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  2   
------
 2    
x  - 1

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

2/(x^2 - 1)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{2} - 1$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. 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:
  
  $- \frac{2 x}{\left(x^{2} - 1\right)^{2}}$
So, the result is: $- \frac{4 x}{\left(x^{2} - 1\right)^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

      /          2 \
      |       2*x  |
-48*x*|-1 + -------|
      |           2|
      \     -1 + x /
--------------------
              3     
     /      2\      
     \-1 + x /

$$- \frac{48 x \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{3}}$$

Simplify

The graph

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Derivative of 2/(x^2-1)

The graph:

Piecewise:

The solution