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: 43

Answer

$f'(x)=-1+\sec^2(x)$.

Work Step by Step

$f(x)=g(x)+h(x)\rightarrow g(x)=-x$ and $h(x)=\tan(x)$. Using the Power Rule: $g'(x)=-1$. By Theorem $2.9$: $\frac{d}{dx}(\tan(x))=\sec^2(x)$. Using the Sum Rule $f'(x)=g'(x)+h'(x)$. $f'(x)=-1+\sec^2(x)$
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