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

Textbook Question

Chapter 2, 2.3 - Problem 35 - 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 rule to evaluate the derivative of the function, such that:

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

`f'(x) = (6x^2 + 5)(x - 3)(x + 2) + (2x^3 + 5x)(x + 2) + (2x^3 + 5x)(x - 3)`

Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = (6x^2 + 5)(x - 3)(x + 2) + (2x^3 + 5x)(x + 2) + (2x^3 + 5x)(x - 3).`

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