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Popular >

derivative of (x-2)(x+2)^3

Solution

derivative of

(x - 2) (x + 2)^{3}

Solution

(x + 2)^{3} + 3 (x + 2)^{2} (x - 2)

Solution steps

\frac{d}{d x} ((x - 2) (x + 2)^{3})

Apply the Product Rule:

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

f = x - 2, g = (x + 2)^{3}

= \frac{d}{d x} (x - 2) (x + 2)^{3} + \frac{d}{d x} ((x + 2)^{3}) (x - 2)

\frac{d}{d x} (x - 2) = 1

\frac{d}{d x} ((x + 2)^{3}) = 3 (x + 2)^{2}

= 1 \cdot (x + 2)^{3} + 3 (x + 2)^{2} (x - 2)

Simplify

= (x + 2)^{3} + 3 (x + 2)^{2} (x - 2)

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Frequently Asked Questions (FAQ)

What is the derivative of (x-2)(x+2)^3 ?
The derivative of (x-2)(x+2)^3 is (x+2)^3+3(x+2)^2(x-2)
What is the first derivative of (x-2)(x+2)^3 ?
The first derivative of (x-2)(x+2)^3 is (x+2)^3+3(x+2)^2(x-2)