Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.8 Implicit Differentiation - 3.8 Exercises: 46

Answer

Slope at $(1,1) = -1$

Work Step by Step

$x^{\frac{2}{3}}+y^{\frac{2}{3}} = 2$ First Derivative: $\frac{2}{3}x^{\frac{-1}{3}} + \frac{2}{3}y^{\frac{-1}{3}}\frac{dy}{dx} = 0$ $\frac{dy}{dx} = \frac{-y^{\frac{1}{3}}}{x^{\frac{1}{3}}}$ Slope at $(1,1)$ $\frac{dy}{dx} = \frac{-1^{\frac{1}{3}}}{1^{\frac{1}{3}}} = -1$
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