`g(x) = ((3x^2 - 2)/(2x + 3))^3` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 32 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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GivenĀ `g(x)=((3x^2-2)/(2x+3))^3`

Find the derivative using the Quotient Rule within the Chain Rule.

`g'(x)=3((3x^2-2)/(2x+3))^2[((2x+3)(6x)-(3x^2-2)(2))/(2x+3)^4]`

`g'(x)=3((3x-2)/(2x+3))^2[(12x^2+18x-6x^2-4)/(2x+3)^4]`

`g'(x)=3((3x-2)/(2x+3))^2[(6x^2+18x-4)/(2x+3)^4]`

`g'(x)=6(3x-2)^2/(2x+3)^2[(3x^2+9x-2)/(2x+3)^4]`

`g'(x)=(6(3x-2)^2(3x^2+9x-2))/((2x+3)^6)`

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