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Popular >

derivative of (x-2^3(x-6))

Solution

\frac{d}{d x} ((x - 2)^{3} (x - 6))

Solution

3 (x - 2)^{2} (x - 6) + (x - 2)^{3}

Solution steps

\frac{d}{d x} ((x - 2)^{3} (x - 6))

Apply the Product Rule:

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

f = (x - 2)^{3}, g = x - 6

= \frac{d}{d x} ((x - 2)^{3}) (x - 6) + \frac{d}{d x} (x - 6) (x - 2)^{3}

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

\frac{d}{d x} (x - 6) = 1

= 3 (x - 2)^{2} (x - 6) + 1 \cdot (x - 2)^{3}

Simplify

= 3 (x - 2)^{2} (x - 6) + (x - 2)^{3}

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Frequently Asked Questions (FAQ)

What is the derivative of (x-2^3(x-6)) ?
The derivative of (x-2^3(x-6)) is 3(x-2)^2(x-6)+(x-2)^3
What is the first derivative of (x-2^3(x-6)) ?
The first derivative of (x-2^3(x-6)) is 3(x-2)^2(x-6)+(x-2)^3