`h(t) = (t + 1)^(2/3) (2t^2 - 1)^3` Find the derivative of the function.

Expert Answers
gsenviro eNotes educator| Certified Educator

Using the product rule of derivative, we can solve this as:

`h'(t) = (2/3) (t+1)^(-1/3) *(1) * (2t^2-1)^3 `

`+ (t+1)^(2/3) * 3*(2t^2-1)^2 * (4t)`

`= (2t^2-1)^2 (t+1)^(-1/3) [ (2/3)(2t^2-1) + (t+1)*(12t)]`

`= (2t^2-1)^2(t+1)^(-1/3)(40/3 t^2 +12t-2/3)`