Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Practice Exercises - Page 178: 45



Work Step by Step

Rewrite the equation: $(xy)^{1/2}=1$ Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x: $\frac{1}{2}(xy)^{-1/2}\times(x\frac{dy}{dx}+y)=0$ Move all terms with dy/dx to one side of the equation, and isolate dy/dx: $x\frac{dy}{dx}+y=0$ $\frac{dy}{dx}=\frac{-y}{x}$
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