Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Review - Exercises - Page 983: 20


$f_{xx}=0$ $f_{yy}=4xe^{-2y}$ $f_{xy}=f_{yx}=-2e^{-2y}$

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: $z_{x}=e^{-2y}$ $z_{y}=-2xe^{-2y}$ Then take the derivative of the first order partial derivatives to find second partial derivatives: $f_{xx}=0$ $f_{yy}=4xe^{-2y}$ Second partial derivatives of first order partial derivative of x with respect to y and y with respect to x are the same: $f_{xy}=f_{yx}=-2e^{-2y}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.