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2*x/(x^2-1)

Derivative of 2*x/(x^2-1)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2*x  
------
 2    
x  - 1
$$\frac{2 x}{x^{2} - 1}$$
(2*x)/(x^2 - 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
               2  
  2         4*x   
------ - ---------
 2               2
x  - 1   / 2    \ 
         \x  - 1/ 
$$- \frac{4 x^{2}}{\left(x^{2} - 1\right)^{2}} + \frac{2}{x^{2} - 1}$$
The second derivative [src]
    /          2 \
    |       4*x  |
4*x*|-3 + -------|
    |           2|
    \     -1 + x /
------------------
             2    
    /      2\     
    \-1 + x /     
$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{2}}$$
The third derivative [src]
   /                    /          2 \\
   |                  2 |       2*x  ||
   |               4*x *|-1 + -------||
   |          2         |           2||
   |       4*x          \     -1 + x /|
12*|-1 + ------- - -------------------|
   |           2               2      |
   \     -1 + x          -1 + x       /
---------------------------------------
                        2              
               /      2\               
               \-1 + x /               
$$\frac{12 \left(- \frac{4 x^{2} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}{x^{2} - 1} + \frac{4 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{2}}$$
The graph
Derivative of 2*x/(x^2-1)