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 - Page 151: 29


$H'(\theta)=\sin \theta+\theta \cos \theta$ $H''(\theta)= 2\cos \theta-\theta \sin \theta$

Work Step by Step

$H'(\theta)= \frac{d}{d\theta}(\theta\sin \theta)= 1\times\sin \theta+\theta\times\cos\theta$ $=\sin \theta+\theta \cos \theta$ $H''(\theta)=\frac{d}{d\theta}(\sin\theta)+\frac{d}{d\theta}(\theta\cos\theta)$ $\cos \theta+ 1\times\cos \theta+ \theta\times-\sin\theta$ $=2\cos \theta-\theta \sin \theta$
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