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1/(x^2-1)^7

Derivative of 1/(x^2-1)^7

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    1    
---------
        7
/ 2    \ 
\x  - 1/ 
$$\frac{1}{\left(x^{2} - 1\right)^{7}}$$
1/((x^2 - 1)^7)
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
      -14*x       
------------------
                 7
/ 2    \ / 2    \ 
\x  - 1/*\x  - 1/ 
$$- \frac{14 x}{\left(x^{2} - 1\right) \left(x^{2} - 1\right)^{7}}$$
The second derivative [src]
   /          2 \
   |      16*x  |
14*|-1 + -------|
   |           2|
   \     -1 + x /
-----------------
             8   
    /      2\    
    \-1 + x /    
$$\frac{14 \left(\frac{16 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{8}}$$
The third derivative [src]
      /         2 \
      |      6*x  |
672*x*|1 - -------|
      |          2|
      \    -1 + x /
-------------------
              9    
     /      2\     
     \-1 + x /     
$$\frac{672 x \left(- \frac{6 x^{2}}{x^{2} - 1} + 1\right)}{\left(x^{2} - 1\right)^{9}}$$
The graph
Derivative of 1/(x^2-1)^7