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Identical expressions
(x^ two - one)^n
(x squared minus 1) to the power of n
(x to the power of two minus one) to the power of n
(x2-1)n
x2-1n
(x²-1)^n
(x to the power of 2-1) to the power of n
x^2-1^n
Similar expressions
(x^2+1)^n

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

Derivative of (x^2-1)^n

The solution

You have entered [src]

        n
/ 2    \ 
\x  - 1/

$$\left(x^{2} - 1\right)^{n}$$

  /        n\
d |/ 2    \ |
--\\x  - 1/ /
dx

$$\frac{\partial}{\partial x} \left(x^{2} - 1\right)^{n}$$

Transform

Detail solution

Let $u = x^{2} - 1$ .
Apply the power rule: $u^{n}$ goes to $\frac{n u^{n}}{u}$
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 $\left(-1\right) 1$ is zero.
  The result is: $2 x$
The result of the chain rule is:

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

$2 n x \left(x^{2} - 1\right)^{n - 1}$

The answer is:

$2 n x \left(x^{2} - 1\right)^{n - 1}$

The first derivative [src]

              n
      / 2    \ 
2*n*x*\x  - 1/ 
---------------
      2        
     x  - 1

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

Simplify

The second derivative [src]

             n /         2          2\
    /      2\  |      2*x      2*n*x |
2*n*\-1 + x / *|1 - ------- + -------|
               |          2         2|
               \    -1 + x    -1 + x /
--------------------------------------
                     2                
               -1 + x

$$\frac{2 n \left(x^{2} - 1\right)^{n} \left(\frac{2 n x^{2}}{x^{2} - 1} - \frac{2 x^{2}}{x^{2} - 1} + 1\right)}{x^{2} - 1}$$

Simplify

The third derivative [src]

               n /                2          2      2  2\
      /      2\  |             4*x      6*n*x    2*n *x |
4*n*x*\-1 + x / *|-3 + 3*n + ------- - ------- + -------|
                 |                 2         2         2|
                 \           -1 + x    -1 + x    -1 + x /
---------------------------------------------------------
                                 2                       
                        /      2\                        
                        \-1 + x /

$$\frac{4 n x \left(x^{2} - 1\right)^{n} \left(\frac{2 n^{2} x^{2}}{x^{2} - 1} - \frac{6 n x^{2}}{x^{2} - 1} + 3 n + \frac{4 x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{2}}$$

Simplify

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Derivative of (x^2-1)^n

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