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: 10

Answer

$y'=\cos^{2}\theta-\sin^{2}\theta$

Work Step by Step

$y=\sin\theta\cos\theta$ Differentiate using the product rule: $y'=(\sin\theta)(\cos\theta)'+(\cos\theta)(\sin\theta)'=...$ $...=(\sin\theta)(-\sin\theta)+(\cos\theta)(cos\theta)=-\sin^{2}\theta+\cos^{2}\theta=\cos^{2}\theta-\sin^{2}\theta$
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