Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises - Page 169: 22


$y'=e^{6x}(\cos x+6\sin x)$

Work Step by Step

$y=e^{6x}\sin x$ Start the differentiation process by applying the product rule: $y'=e^{6x}(\sin x)'+(e^{6x})'\sin x=...$ Evaluate the indicated derivatives and simplify: $...=e^{6x}\cos x+6e^{6x}\sin x=...$ Take out common factor $e^{6x}$: $...=e^{6x}(\cos x+6\sin x)$
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