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Derivative of (x^2-1)/x
Identical expressions
one /(x^ two - one)^ seven
1 divide by (x squared minus 1) to the power of 7
one divide by (x to the power of two minus one) to the power of seven
1/(x2-1)7
1/x2-17
1/(x²-1)⁷
1/(x to the power of 2-1) to the power of 7
1/x^2-1^7
1 divide by (x^2-1)^7
Similar expressions
1/(x^2+1)^7

The derivative of the function/ 1/(x^2-1)^7

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

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

Let $u = \left(x^{2} - 1\right)^{7}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 1\right)^{7}$ :
1. Let $u = x^{2} - 1$ .
2. Apply the power rule: $u^{7}$ goes to $7 u^{6}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 1\right)$ :
  1. Differentiate $x^{2} - 1$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of the constant $-1$ is zero.
    The result is: $2 x$
  The result of the chain rule is:
  
  $14 x \left(x^{2} - 1\right)^{6}$
The result of the chain rule is:

$- \frac{14 x}{\left(x^{2} - 1\right)^{8}}$
Now simplify:

$- \frac{14 x}{\left(x^{2} - 1\right)^{8}}$

The answer is:

$- \frac{14 x}{\left(x^{2} - 1\right)^{8}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      -14*x       
------------------
                 7
/ 2    \ / 2    \ 
\x  - 1/*\x  - 1/

$$- \frac{14 x}{\left(x^{2} - 1\right) \left(x^{2} - 1\right)^{7}}$$

Simplify

The second derivative [src]

   /          2 \
   |      16*x  |
14*|-1 + -------|
   |           2|
   \     -1 + x /
-----------------
             8   
    /      2\    
    \-1 + x /

$$\frac{14 \left(\frac{16 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{8}}$$

Simplify

The third derivative [src]

      /         2 \
      |      6*x  |
672*x*|1 - -------|
      |          2|
      \    -1 + x /
-------------------
              9    
     /      2\     
     \-1 + x /

$$\frac{672 x \left(- \frac{6 x^{2}}{x^{2} - 1} + 1\right)}{\left(x^{2} - 1\right)^{9}}$$

Simplify

The graph

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

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The solution