Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises - Page 196: 3


$f'(x)=e^{x}(\cos x-\sin x)$

Work Step by Step

$f(x)=e^{x}\cos x$ Differentiate using the product rule: $f'(x)=(e^{x})(\cos x)'+(\cos x)(e^{x})'=-e^{x}\sin x+e^{x}\cos x=...$ Take out common factor $e^{x}$ to obtain a better looking answer (Optional) $...=e^{x}(\cos x-\sin x)$
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