`f(x) = x(2x - 5)^3` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 24 - 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)'(2x - 5)^3 + (x)((2x - 5)^3)'`

`f'(x) = (2x - 5)^3 + 3x((2x - 5)^2)*(2x - 5)'`

Factoring out `(2x - 5)^2` yields:

`f'(x) = (2x - 5)^2(2x - 5 + 6x)`

`f'(x) = (2x - 5)^2(8x - 5)`

Hence, evaluating the derivative of the function, using the product rule, yields f`'(x) = (2x - 5)^2(8x - 5).`

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