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-2x/(x^2-1)^2

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   -2*x  
---------
        2
/ 2    \ 
\x  - 1/ 
$$- \frac{2 x}{\left(x^{2} - 1\right)^{2}}$$
d /   -2*x  \
--|---------|
dx|        2|
  |/ 2    \ |
  \\x  - 1/ /
$$\frac{d}{d x} \left(- \frac{2 x}{\left(x^{2} - 1\right)^{2}}\right)$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the quotient rule, which is:

      and .

      To find :

      1. Apply the power rule: goes to

      To find :

      1. Let .

      2. Apply the power rule: goes to

      3. Then, apply the chain rule. Multiply by :

        1. Differentiate term by term:

          1. The derivative of the constant is zero.

          2. Apply the power rule: goes to

          The result is:

        The result of the chain rule is:

      Now plug in to the quotient rule:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
                    2  
      2          8*x   
- --------- + ---------
          2           3
  / 2    \    / 2    \ 
  \x  - 1/    \x  - 1/ 
$$\frac{8 x^{2}}{\left(x^{2} - 1\right)^{3}} - \frac{2}{\left(x^{2} - 1\right)^{2}}$$
The second derivative [src]
    /         2 \
    |      6*x  |
8*x*|3 - -------|
    |          2|
    \    -1 + x /
-----------------
             3   
    /      2\    
    \-1 + x /    
$$\frac{8 x \left(- \frac{6 x^{2}}{x^{2} - 1} + 3\right)}{\left(x^{2} - 1\right)^{3}}$$
The third derivative [src]
   /                   /          2 \\
   |                 2 |       8*x  ||
   |              2*x *|-3 + -------||
   |         2         |           2||
   |      6*x          \     -1 + x /|
24*|1 - ------- + -------------------|
   |          2               2      |
   \    -1 + x          -1 + x       /
--------------------------------------
                       3              
              /      2\               
              \-1 + x /               
$$\frac{24 \cdot \left(\frac{2 x^{2} \cdot \left(\frac{8 x^{2}}{x^{2} - 1} - 3\right)}{x^{2} - 1} - \frac{6 x^{2}}{x^{2} - 1} + 1\right)}{\left(x^{2} - 1\right)^{3}}$$
The graph
Derivative of -2x/(x^2-1)^2