Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 13 - Partial Derivatives - 13.3 Partial Derivatives - Exercises Set 13.3 - Page 937: 28


$z_x=ye^{xy}sin(4y^2)$ $z_y=8ye^{xy}cos(4y^2)+xe^{xy}sin(4y^2)$

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: $z_x=e^{xy}sin(4y^2)*y=ye^{xy}sin(4y^2)$ $z_y=e^{xy}*cos(4y^2)*8y+e^{xy}sin(4y^2)*x=8ye^{xy}cos(4y^2)+xe^{xy}sin(4y^2)$
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