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: 46

Answer

$h'(x)=-\dfrac{1}{x^2}-12\sec(x)\tan(x)$.

Work Step by Step

$h(x)=f(x)+g(x)\rightarrow f(x)=\dfrac{1}{x}$; $g(x)=-12\sec(x)$. Using the Power Rule: $f'(x)=(-1)(x^{-1-1})=-\dfrac{1}{x^2}$. By Theorem 2.9 and the Constant Multiple Rule: $g'(x)=-12(\dfrac{d}{dx}\sec(x))=-12\sec(x)\tan(x)$. Using the Sum Rule: $h'(x)=f'(x)+g'(x)=-\dfrac{1}{x^2}-12\sec(x)\tan(x)$.
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