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: 20

Answer

$$z_x = \sin{(xy)} + x y \cos{(xy)}.$$ $$z_y = x^2 \cos{(xy)}.$$

Work Step by Step

To find $z_x$, we treat $y$ as a constant and differentiate with respect to $x$. Using the product rule, we have $$z_x = 1 \cdot \sin{(xy)} + x \cdot y \cos{(xy)}.$$ Similarly, to find $z_y$, we treat $x$ as constant and differentiate with respect to $y$. Thus $$z_y = x \cdot x \cos{(xy)} = x^2 \cos{(xy)}.$$
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.