Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.8 Implicit Differentiation - Exercises - Page 154: 59


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Work Step by Step

Implicitly differentiating $xy=1$ with respect to $t$, we have $\frac{dx}{dt}\times y+ x\frac{dy}{dt}=0$ $\implies x \frac{dy}{dt}=-y\frac{dx}{dt}$ $\implies \frac{dy}{dt}=-\frac{y}{x}\frac{dx}{dt}$
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