Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 23


$$ R'(\theta)=\frac{-4\sin \theta}{(4+\cos \theta)^2}.$$

Work Step by Step

Since $ R(\theta)=\frac{\cos\theta}{4+\cos \theta}$, then using the quotient rule, we have $$ R'(\theta)=\frac{(4+\cos \theta)(-\sin \theta)-\cos \theta (-\sin \theta)}{(4+\cos \theta)^2}=\frac{-4\sin \theta}{(4+\cos \theta)^2}.$$
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