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: 11

Answer

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

Work Step by Step

Differentiate using quotient rule and the trig rules. $f'(\theta ) = \frac{\sin \theta '(1+\cos \theta) - \sin \theta (\cos \theta ') }{(1 +\cos \theta)^2}$ $= \frac{\cos \theta(1+\cos \theta) - \sin \theta (-\sin \theta)}{(1 +\cos \theta)^2}$ $=\frac{\cos \theta + \cos ^2 \theta +\sin ^2 \theta}{(1 +\cos \theta)^2}$ Simplify using trig identities $=\frac{1+\cos \theta}{(1 +\cos \theta)^2}$ $=\frac {1}{1+\cos \theta}$
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