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x^3/(x^2-1)

Derivative of x^3/(x^2-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3  
  x   
------
 2    
x  - 1
$$\frac{x^{3}}{x^{2} - 1}$$
x^3/(x^2 - 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    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]
        4         2 
     2*x       3*x  
- --------- + ------
          2    2    
  / 2    \    x  - 1
  \x  - 1/          
$$- \frac{2 x^{4}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x^{2}}{x^{2} - 1}$$
The second derivative [src]
    /                 /          2 \\
    |               2 |       4*x  ||
    |              x *|-1 + -------||
    |         2       |           2||
    |      6*x        \     -1 + x /|
2*x*|3 - ------- + -----------------|
    |          2              2     |
    \    -1 + x         -1 + x      /
-------------------------------------
                     2               
               -1 + x                
$$\frac{2 x \left(\frac{x^{2} \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{x^{2} - 1} - \frac{6 x^{2}}{x^{2} - 1} + 3\right)}{x^{2} - 1}$$
The third derivative [src]
  /                   /          2 \        /          2 \\
  |                 4 |       2*x  |      2 |       4*x  ||
  |              4*x *|-1 + -------|   3*x *|-1 + -------||
  |         2         |           2|        |           2||
  |      6*x          \     -1 + x /        \     -1 + x /|
6*|1 - ------- - ------------------- + -------------------|
  |          2                 2                   2      |
  |    -1 + x         /      2\              -1 + x       |
  \                   \-1 + x /                           /
-----------------------------------------------------------
                                2                          
                          -1 + x                           
$$\frac{6 \left(- \frac{4 x^{4} \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{2}} + \frac{3 x^{2} \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{x^{2} - 1} - \frac{6 x^{2}}{x^{2} - 1} + 1\right)}{x^{2} - 1}$$
The graph
Derivative of x^3/(x^2-1)