`g(x) = (2x^3 + 5x)(3x - 4)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that:

`f'(x) = (2x^3 + 5x)'(3x-4) + (2x^3 + 5x)(3x-4)'`

`f'(x) = (6x^2 + 5)(3x-4) + (2x^3 + 5x)(3 - 0)`

`f'(x) = 18x^3 - 24x^2 + 15x - 20 + 6x^3 + 15x`

Combining like terms yields:

`f'(x) = 24x^3 - 24x^2 + 30x - 20`

Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = 24x^3 - 24x^2 + 30x - 20.`