Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises: 15

Answer

Differentiate $f(\theta ) = \theta \cos \theta \sin \theta$ $f'(\theta)= \frac{1}{2}\sin 2\theta +\theta\cos 2\theta$

Work Step by Step

Use the product rule and trig rules. $f'(\theta) = \cos \theta \sin \theta - \theta \sin ^2 \theta + \theta \cos ^2\theta$ $=\cos \theta \sin \theta +\theta(\cos ^2 \theta - \sin ^2 \theta)$ Use trig identities to simplify $= \frac{1}{2}\sin 2\theta +\theta\cos 2\theta$
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