Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.6 Implicit Differentiation - 2.6 Exercises: 18

Answer

$\frac{dy}{dx} = \frac{-\sin y -y\cos x}{x\cos y + \sin x}$

Work Step by Step

$x\sin y + y\sin x = 1$ Differentiate both sides with respect to x $\sin y + \frac{dy}{dx}x\cos y + \frac{dy}{dx}\sin x + y \cos x = 0$ Isolate $\frac{dy}{dx}$ $\frac{dy}{dx}x\cos y+ \frac{dy}{dx}\sin x = -\sin y - y\cos x$ $\frac{dy}{dx} (x\cos y + \sin x) = (-\sin y - y\cos x)$ $\frac{dy}{dx} = \frac{-\sin y -y\cos x}{x\cos y + \sin x}$
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