Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - 14.1 Functions of Several Variables - 14.1 Exercises - Page 940: 17


The domain is $$\mathcal{D}=\{(x,y)|y\neq-x\}.$$ It is shown in the figure below. The domain is in light blue and the red line is excluded from it.

Work Step by Step

The only constraint we have is that the denominator has to be different than zero which gives $x+y\neq0$ or $y\neq-x$, so the domain $$\mathcal{D}=\{(x,y)|y\neq-x\}$$ is the $xy$ plane with the line $y=-x$ excluded, and it is sketched in the figure below (the red line representing $y=-x$ is excluded, the region is light blue).
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