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Derivative of:
Derivative of x/(2*x-1)
Derivative of (x^2+1)/(x^2-1)
Derivative of x^3/x
Derivative of x^2+4
Graphing y =:
(x^2-1)^3
Integral of d{x}:
(x^2-1)^3
Identical expressions
(x^ two - one)^ three
(x squared minus 1) cubed
(x to the power of two minus one) to the power of three
(x2-1)3
x2-13
(x²-1)³
(x to the power of 2-1) to the power of 3
x^2-1^3
Similar expressions
(x^2+1)^3

The derivative of the function/ (x^2-1)^3

Derivative of (x^2-1)^3

The solution

You have entered [src]

        3
/ 2    \ 
\x  - 1/

\left(x^{2} - 1\right)^{3}

(x^2 - 1)^3

Detail solution

Let $u = x^{2} - 1$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
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:

$6 x \left(x^{2} - 1\right)^{2}$
Now simplify:

$6 x \left(x^{2} - 1\right)^{2}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            2
    / 2    \ 
6*x*\x  - 1/

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

Simplify

The second derivative [src]

  /      2\ /        2\
6*\-1 + x /*\-1 + 5*x /

6 \left(x^{2} - 1\right) \left(5 x^{2} - 1\right)

Simplify

The third derivative [src]

     /        2\
24*x*\-3 + 5*x /

24 x \left(5 x^{2} - 3\right)

Simplify

The graph

Derivative of (x^2-1)^3