Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.3 Partial Derivatives - 14.3 Exercises - Page 967: 101



Work Step by Step

Consider, we have $f_{xyy}=(f_{xy})_{y}$ ...(1) $f_{yxy}=(f_{yx})_{y}$ ...(2) From the equations (1) and (2), we get $(f_{xy})_{y}=(f_{xy})_{y}=f_{xyy}$ This yields: $f_{yxy}=f_{xyy}$ Since, $ f_{yyx}=(f_{y})_{yx}\\(f_{y})_{yx}$=$(f_{y})_{xy}$ Thus, we have $f_{yyx}=(f_{y})_{xy}=f_{yxy}$ $\implies f_{yxy}=f_{yxy},$ Transitive property of equality defines as: $f_{xyy}=f_{yxy}=f_{yyx}$
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.