Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.3 Exercises - Page 896: 8

Answer

$$\frac{\partial f(x,y)}{\partial x}=2x$$ $$\frac{\partial f(x,y)}{\partial y}=-4y$$

Work Step by Step

The partial derivative with respect to $x$ is: $$\frac{\partial f(x,y)}{\partial x}=\frac{\partial}{\partial x}(x^2-2y^2+4)=2x$$ because $y$ is treated as a constant. The partial derivative with respect to $y$ is: $$\frac{\partial f(x,y)}{\partial y}=\frac{\partial}{\partial y}(x^2-2y^2+4)=-4y$$ because now $x$ is treated as a constant.
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