University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Section 3.7 - Implicit Differentiation - Exercises - Page 164: 9


$$\frac{dy}{dx}=\cos y\cot y$$

Work Step by Step

$$x=\sec y$$ 1) Differentiate both sides of the equation with respect to $x$: $$\frac{dx}{dx}=\frac{d}{dx}(\sec y)$$ $$1=\sec y\tan y\frac{dy}{dx}$$ 2) Now solve for $dy/dx$: $$\frac{dy}{dx}=\frac{1}{\sec y\tan y}=\frac{1}{\sec y}\times\frac{1}{\tan y}$$ $$\frac{dy}{dx}=\frac{1}{\frac{1}{\cos y}}\times\cot y=\cos y\cot y$$
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