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Popular Calculus >

derivative of f(x)=x^2(x^2-8)

Solution

derivative of

f (x) = x^{2} (x^{2} - 8)

Solution

4 x^{3} - 16 x

Solution steps

\frac{d}{d x} (x^{2} (x^{2} - 8))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = x^{2} - 8

= \frac{d}{d x} (x^{2}) (x^{2} - 8) + \frac{d}{d x} (x^{2} - 8) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (x^{2} - 8) = 2 x

= 2 x (x^{2} - 8) + 2 x x^{2}

Simplify

2 x (x^{2} - 8) + 2 x x^{2} : 4 x^{3} - 16 x

= 4 x^{3} - 16 x

Graph

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\int (2 x - 5)^{- \frac{1}{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2(x^2-8) ?
The derivative of f(x)=x^2(x^2-8) is 4x^3-16x
What is the first derivative of f(x)=x^2(x^2-8) ?
The first derivative of f(x)=x^2(x^2-8) is 4x^3-16x