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



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.
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