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y=(x²-4)³
The derivative of the function/ y=(x²-4)³

Derivative of y=(x²-4)³

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        3
/ 2    \ 
\x  - 4/
$$\left(x^{2} - 4\right)^{3}$$ 
  /        3\
d |/ 2    \ |
--\\x  - 4/ /
dx
$$\frac{d}{d x} \left(x^{2} - 4\right)^{3}$$
Transform
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            2
    / 2    \ 
6*x*\x  - 4/
$$6 x \left(x^{2} - 4\right)^{2}$$
Simplify
The second derivative [src] 
  /      2\ /        2\
6*\-4 + x /*\-4 + 5*x /
$$6 \left(x^{2} - 4\right) \left(5 x^{2} - 4\right)$$
Simplify
The third derivative [src] 
     /         2\
24*x*\-12 + 5*x /
$$24 x \left(5 x^{2} - 12\right)$$
Simplify
The graph
Derivative of y=(x²-4)³
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