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: 12

Answer

Differentiate $y=\frac{\cos x}{1-\sin x}$ $y'=\frac{1}{1-\sin x}$

Work Step by Step

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