Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 9 - Multiveriable Calculus - 9.2 Partial Derivatives - 9.2 Exercises - Page 478: 2


a. $\frac{\partial g}{\partial x}=12y$ or $\frac{\partial g}{\partial x}=12x$; b. $\frac{\partial g}{\partial y}=4$ or $\frac{\partial g}{\partial y}=12x$; c. 54; d. 32.

Work Step by Step

$g_{x}(x,y) =8+12xy$ $g_{y}(x,y)=6x^{2}+4y$ a. $\frac{\partial g}{\partial x}=g_{xx}(x,y)=12y$ $\frac{\partial g}{\partial x}=g_{xy}(x,y)=12x$ b. $\frac{\partial g}{\partial y}=g_{yy}(x,y)=4$ $\frac{\partial g}{\partial y}=g_{yx}(x,y)=12x$ c. Since $\frac{\partial z}{\partial x}=6x^{2} + 4y$ $\frac{\partial z}{\partial x}(-3,0)=6(-3)^{2}+4(0)=54$ d. $g_{x}(2,1)=8+12(2)(1)=32$
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