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: 17

Answer

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.
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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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