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: 54


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

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: $w_x=siny+ycosx+y \\w_y=x \space cosy+\sin (x)+x$ Now, find the second partial derivatives. $w_{xy}=\cos y+\cos x+1 \\w_{yx}=cosy+cosx+1$
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