University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 202: 63



Work Step by Step

Given that: $y=\csc^{-1}({sec\theta})$ differentiate with respect to $\theta$: $\frac{dy}{d{\theta}}=\frac{\frac{d\sec{\theta}}{d{\theta}}}{|sec{\theta}|{\sqrt{\sec^2{\theta}-1}}}$ $\frac{dy}{d{\theta}}=\frac{{-\tan{\theta}\sec{\theta}}}{|sec{\theta}|{\sqrt{\sec^2{\theta}-1}}}$ $\frac{dy}{d{\theta}}=\frac{{-\tan{\theta}}}{\tan{\theta}}$ $\frac{dy}{d{\theta}}=-1$
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