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Popular >

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

Solution

\frac{d}{d x} ((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)

Graph

Popular Examples

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\frac{c ^{4} - x ^{4}}{c ^{4} + x ^{4}}

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\int sin (x^{3}) x^{2} d x

integral of (1-x)/(x^2)

\int \frac{1 - x}{x ^{2}} d x

limit as x approaches 0-of (x-1)/(x^2)

x \to 0 - lim (\frac{x - 1}{x ^{2}})

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)