`h(x) = ((x+5)/(x^2 + 3))^2` Find the derivative of the function.

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Chapter 2, Review - Problem 64 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `h(x)=((x+5)/(x^2+3))^2`

To find the derivative of the function use the Quotient Rule within the Chain Rule.

`h(x)=2((x+5)/(x^2+3))[((x^2+3)(1)-(x+5)(2x))/(x^+3)^2]`

`h'(x)=2((x+5)/(x^2+3))[(x^2+3-2x^2-10x)/(x^2+3)^2]`

`h'(x)=2((x+5)/(x^2+3))[(-x^2-10x+3)/(x^2+3)^2]`

`h'(x)=(-2(x+5)(x^2+10x-3))/((x^2+3)^3)`

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