Mister exam

Derivatives y=(x²-1)³

Function f() - derivative -N order

The graph:

from to

Enter:

The solution

You have entered [src]
        3
/ 2    \ 
\x  - 1/ 
$$\left(x^{2} - 1\right)^{3}$$
(x^2 - 1)^3
Detail solution
  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:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
            2
    / 2    \ 
6*x*\x  - 1/ 
$$6 x \left(x^{2} - 1\right)^{2}$$
The second derivative [src]
  /      2\ /        2\
6*\-1 + x /*\-1 + 5*x /
$$6 \left(x^{2} - 1\right) \left(5 x^{2} - 1\right)$$
The third derivative [src]
     /        2\
24*x*\-3 + 5*x /
$$24 x \left(5 x^{2} - 3\right)$$
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