`f(x) = (x^3 - x)(x^2 + 2)(x^2 + x - 1)` Find the derivative of the algebraic function.

Textbook Question

Chapter 2, 2.3 - Problem 36 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Since the function is a product, you need to find the derivative using the product rule, such that:

`f'(x) = (x^3- x)'(x^2 + 2)(x^2 + x - 1) + (x^3- x)(x^2 + 2)'(x^2 + x - 1) + (x^3- x)(x^2 + 2)(x^2 + x - 1)'`

`f'(x) = (3x^2 - 1)(x^2 + 2)(x^2 + x - 1) + (x^3- x)(2x)(x^2 + x - 1) + (x^3- x)(x^2 + 2)(2x + 1)`

Hence, evaluating the derivative of the function yields `f'(x) = (3x^2 - 1)(x^2 + 2)(x^2 + x - 1) + (x^3- x)(2x)(x^2 + x - 1) + (x^3- x)(x^2 + 2)(2x + 1).`

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