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 - Page 166: 5


For $x^2-4xy +y^2=4$, find $\frac{dy}{dx}$ by implicit differentiation $\frac{dy}{dx}=\frac{2y-x}{x-2y}$

Work Step by Step

Differentiate both sides with respect to $x$. $2x -4(y+x\frac{dy}{dx}) +2y\frac{dy}{dx} = 0$ Isolate $\frac{dy}{dx}$ $2x-4y-4x\frac{dy}{dx} +2y\frac{dy}{dx} =0$ $\frac{dy}{dx}(2y-4x) = 4y-2x$ $\frac{dy}{dx}=\frac{4y-2x}{2y-4x}$ $\frac{dy}{dx}=\frac{2y-x}{x-2y}$
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