Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises: 129

Answer

False

Work Step by Step

Counter-example: $f(x)=(x-1)(x+1)\rightarrow g(x)=(x-1)$; $h(x)=(x+1)$ $g'(x)=1$; $h'(x)=1\rightarrow$ If it was true $f'(x)=1$ But by expanding we see that $f(x)=x^2-1\rightarrow f'(x)=2x.$ The rule is therefore false. Also, it contradicts the product rule.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.