Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.5 Exercises: 24

Answer

$\dfrac{dy}{dx}=-\dfrac{\sqrt[3]{y}}{\sqrt[3]{x}}.$ $\dfrac{dy}{dx}=-\dfrac{1}{2}.$

Work Step by Step

$\dfrac{d}{dx}(x^{\frac{2}{3}})+\dfrac{d}{dx}(y^{\frac{2}{3}})=\dfrac{d}{dx}(5)\rightarrow$ $\dfrac{2}{3\sqrt[3]{x}}+\dfrac{dy}{dx}(\dfrac{2}{3\sqrt[3]{y}})=0\rightarrow$ $\dfrac{dy}{dx}=-\dfrac{\sqrt[3]{y}}{\sqrt[3]{x}}.$ At $(8, 1)\rightarrow\dfrac{dy}{dx}=-\dfrac{\sqrt[3]{1}}{\sqrt[3]{8}}=-\dfrac{1}{2}.$
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