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


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

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 $$z_y = x \cdot x \cos{(xy)} = x^2 \cos{(xy)}.$$
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