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

Question

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

 

Here's what I did using the chain and product rules:

 

2/3(t + 1)^-1/3 * (2t² - 1)³ + 3(2t² - 1)² * 4t * (t + 1)^2/3

 

2(2t² - 1)³    

________         +        12t(2t² - 1)(t + 1)^2/3

3(t + 1)²

 

But this isn't the right answer (see below). What am I doing wrong?

 

#19, p205

ANSWER: h'(t) = 2/3(t + 1)^-1/3 (2t² + 18t - 1)

Answer 1

Your work for the product rule using chain rule is correct.   First step is great.

 

There is a common factor (GCF) among the terms of the derivative.  The GCF is  (t + 1)^-1/3 (2t² - 1)² .

 

 

(t + 1)^-1/3 (2t² - 1)² [(2/3)(2t² - 1) + 12t(t + 1)]

 

 

Simplify the terms in bold brackets, then multiply them by the GCF.