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Popular >

derivative of y=x(x-2)^3

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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