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

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Chapter 2, 2.4 - Problem 30 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `h(t)=((t^2)/(t^3+2))^2`

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

`h'(t)=2[(t^2)/(t^3+2)][((t^3+2)(2t)-(t^2)(3t^2))/(t^3+2)^2]`

`h'(t)=2[(t^2)/(t^3+2)][((2t^4+4t)-(3t^4))/(t^3+2)^2]`

`h'(t)=2[(t^2)/(t^3+2)][((-t^4+4t))/(t^3+2)^2]`

`h'(t)=-2t[(t^2)/(t^3+2)][(t^3-4)/(t^3+2)^2]`

`h'(t)=((-2t^3)(t^3-4))/(t^3+2)^3`

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