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

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mathace | (Level 3) Assistant Educator

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Given: `g(x)=((x+5)/(x^2+2))^2`

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

`g'(x)=2[(x+5)/(x^2+2)][[(x^2+2)(1)-(x+5)(2x)]/(x^2+2)^2]`

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

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

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

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