Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - Review Exercises - Page 158: 80

Answer

$$\frac{dy}{dx}=\frac{2\sqrt{xy}-y}{x + 8\sqrt{xy}}$$

Work Step by Step

Step-1: Differentiate the following equation with respect to $x$, $$\sqrt{xy}=x-4y$$, we get, $$\frac{1}{2\sqrt{xy}}\cdot\bigg(y+x\frac{dy}{dx}\bigg)=1-4\frac{dy}{dx}$$ Step-2: Isolate $\frac{dy}{dx}$ terms together, $$\frac{dy}{dx}\bigg( \frac{x}{2\sqrt{xy}}+4 \bigg)=1-\frac{y}{2\sqrt{xy}}$$ $$\implies \frac{dy}{dx}=\frac{2\sqrt{xy}-y}{x + 8\sqrt{xy}}$$
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