Answer
$-\ln2-1$
Work Step by Step
$2xy+e^{x+y}-2=0$
$2ydx+2xdy+e^{x+y}dx+e^{x+y}dy=0$
$2\ln2dx+e^{\ln2}dx+e^{\ln2}dy=0$ when $x=0,y=\ln2$
$2\ln2dx+2dx+2dy=0$
$2dy=-(2\ln2+2)dx$
$\frac{dy}{dx}=-(\ln2+1)$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 14: Partial Derivatives - Practice Exercises - Page 865: 36
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