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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
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The solution

You have entered [src] 
        3
/ 2    \ 
\x  - 4/
(x2−4)3\left(x^{2} - 4\right)^{3} 
  /        3\
d |/ 2    \ |
--\\x  - 4/ /
dx
ddx(x2−4)3\frac{d}{d x} \left(x^{2} - 4\right)^{3}
Transform
Detail solution

  1. Let u=x2−4u = x^{2} - 4.

  2. Apply the power rule: u3u^{3} goes to 3u23 u^{2}

  3. Then, apply the chain rule. Multiply by ddx(x2−4)\frac{d}{d x} \left(x^{2} - 4\right):

    1. Differentiate x2−4x^{2} - 4 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant (−1)4\left(-1\right) 4 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    6x(x2−4)26 x \left(x^{2} - 4\right)^{2}

  4. Now simplify:

    6x(x2−4)26 x \left(x^{2} - 4\right)^{2}

The answer is:

6x(x2−4)26 x \left(x^{2} - 4\right)^{2}

The graph
02468-8-6-4-2-1010-20000002000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            2
    / 2    \ 
6*x*\x  - 4/
6x(x2−4)26 x \left(x^{2} - 4\right)^{2}
Simplify
The second derivative [src] 
  /      2\ /        2\
6*\-4 + x /*\-4 + 5*x /
6(x2−4)(5x2−4)6 \left(x^{2} - 4\right) \left(5 x^{2} - 4\right)
Simplify
The third derivative [src] 
     /         2\
24*x*\-12 + 5*x /
24x(5x2−12)24 x \left(5 x^{2} - 12\right)
Simplify
The graph
Derivative of y=(x²-4)³
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