Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.6 Implicit Differentiation - 2.6 Exercises - Page 167: 28



Work Step by Step

$x^{2}+2xy+y^2=12$ $2x+2xy'+2y+8yy'=0$ $2xy'+8yy'=-2x-2y$ $x+4yy'=-x-y$ $y'=-\frac{x+y}{x+4y}$ When $x=2$ and $y=1$, we have $y'=-\frac{2+1}{2+4}=-\frac{1}{2}$, so the equation of the tagent line is $y-1=-\frac{1}{2}(x-2)$, which is $y=-\frac{1}{2}x+2$
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