University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.3 - Partial Derivatives - Exercises - Page 702: 52


$w_{xy}=w_{yx}=\dfrac{1}{y}+\dfrac{1}{x} $

Work Step by Step

Our aim is to take the first partial derivative of the given function $w(x,y)$ with respect to $x$, by treating $y$ as a constant and vice versa: $w_x=e^x+\ln y+\dfrac{y}{x} \\w_y=\dfrac{x}{y}+\ln(x)$ The second partial derivatives are: $w_{xy}=\dfrac{1}{y}+\dfrac{1}{x} \\w_{yx}=\dfrac{1}{y}+\dfrac{1}{x} $
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