Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises: 40

Answer

$$g'(u)=4[(u^2-1)^6-3u]^3(12u(u^2-1)^5-3)$$

Work Step by Step

$$g'(u)=\left([(u^2-1)^6-3u]^4\right)'=4[(u^2-1)^6-3u]^3((u^2-1)^6-3u)'= 4[(u^2-1)^6-3u]^3(6(u^2-1)^5(u^2-1)'-3)= 4[(u^2-1)^6-3u]^3(6(u^2-1)^5\cdot2u-3)=4[(u^2-1)^6-3u]^3(12u(u^2-1)^5-3)$$
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