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 166: 55



Work Step by Step

Given $x=\sin{y}$, differentiate the equation with respect to x: $1=\cos{y}\frac{dy}{dx}$ $\frac{dy}{dx}=\frac{1}{\cos{y}}$ $\cos{y}=\sqrt{(1-\sin^2{y})}=\sqrt{(1-x^2)}$ $\frac{dy}{dx}=\frac{1}{\sqrt{(1-x^2)}}$
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