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: 32

Answer

$\dfrac{dy}{dx}=\dfrac{4}{5}$

Work Step by Step

$\dfrac{d}{dx}(x^3)+\dfrac{d}{dx}(y^3)-\dfrac{d}{dx}(6xy)=0\rightarrow$ $3x^2+\dfrac{dy}{dx}(3y^2)-(6y+\dfrac{dy}{dx}(6x))=0\rightarrow$ $3x^2-6y=\dfrac{dy}{dx}(6x-3y^2)\rightarrow$ $\dfrac{dy}{dx}=\dfrac{x^2-2y}{2x-y^2}.$ At $(\dfrac{4}{3}, \dfrac{8}{3})\rightarrow\dfrac{dy}{dx}=\dfrac{(\frac{4}{3})^2-2(\frac{8}{3})}{2(\frac{4}{3})-(\frac{8}{3})^2}=\dfrac{4}{5}.$
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