Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 44


$h_{xx}=0$ $h_{yy}=xe^y$ $h_{xy}=h_{yx}=e^y$

Work Step by Step

Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa: $h_x=e^y$ $h_y=xe^y+1$ Then take the derivative of the first order partial derivatives to find second partial derivatives: $h_{xx}=0$ $h_{yy}=xe^y$ Second partial derivatives of first order partial derivative of x with respect to y and y with respect to x are the same: $h_{xy}=h_{yx}=e^y$
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