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: 53



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: $w_x=y^2+2xy^3+3x^2y^4 \\w_y=2xy+3x^2y^2+4x^3y^3$ Now, second partial derivatives are: $w_{xy}=w_{yx}=2y+6xy^2+12x^2y^3$
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