`f(x) = (x^2)(x - 2)^4` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 23 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the product and chain rules to evaluate the derivative of the function, such that:

`f'(x) = (x^2)'(x - 2)^4 + (x^2)((x - 2)^4)'`

`f'(x) = (2x)(x - 2)^4 + 4(x^2)((x - 2)^3)*(x-2)'`

Factoring out 2`x(x-2)^3` yields:

`f'(x) = (2x)(x - 2)^3 (x - 2 + 2x)`

`f'(x) = (2x)(x - 2)^3 (3x - 2)`

Hence, evaluating the derivative of the function, using the product rule, yields` f'(x) = (2x)(x - 2)^3 (3x - 2).`

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