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Derivative of 4x/(x^2-1)^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   4*x   
---------
        2
/ 2    \ 
\x  - 1/ 
$$\frac{4 x}{\left(x^{2} - 1\right)^{2}}$$
(4*x)/(x^2 - 1)^2
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. 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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
                  2  
    4         16*x   
--------- - ---------
        2           3
/ 2    \    / 2    \ 
\x  - 1/    \x  - 1/ 
$$- \frac{16 x^{2}}{\left(x^{2} - 1\right)^{3}} + \frac{4}{\left(x^{2} - 1\right)^{2}}$$
The second derivative [src]
     /          2 \
     |       6*x  |
16*x*|-3 + -------|
     |           2|
     \     -1 + x /
-------------------
              3    
     /      2\     
     \-1 + x /     
$$\frac{16 x \left(\frac{6 x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{3}}$$
The third derivative [src]
   /                    /          2 \\
   |                  2 |       8*x  ||
   |               2*x *|-3 + -------||
   |          2         |           2||
   |       6*x          \     -1 + x /|
48*|-1 + ------- - -------------------|
   |           2               2      |
   \     -1 + x          -1 + x       /
---------------------------------------
                        3              
               /      2\               
               \-1 + x /               
$$\frac{48 \left(- \frac{2 x^{2} \left(\frac{8 x^{2}}{x^{2} - 1} - 3\right)}{x^{2} - 1} + \frac{6 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{3}}$$