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: 26

Answer

$\frac{dy}{dx}=\frac{2y-x^2}{y^2-2x}$ Derivative at $(2,3)$ is $\frac{2}{5}$.

Work Step by Step

$x^3+y^3=6xy-1$ $\frac{d}{dx}[x^3+y^3]=\frac{d}{dx}[6xy-1]$ $3x^2+3y^2\frac{dy}{dx}=6y+6x\frac{dy}{dx}$ $(3y^2-6x)\frac{dy}{dx}=6y-3x^2$ $\frac{dy}{dx}=\frac{6y-3x^2}{3y^2-6x}$ $\frac{dy}{dx}=\frac{2y-x^2}{y^2-2x}$ $(2,3)$ $\frac{2y-x^2}{y^2-2x}=\frac{2(3)-(2)^2}{(3)^2-2(2)}=\frac{2}{5}$
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