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: 26


$z_x=-5x^4y^4sin(x^5y^4)$ $z_y=-4x^5y^3sin(x^5y^4)$

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: $z_x=-sin(x^5y^4)*5x^4y^4=-5x^4y^4sin(x^5y^4)$ $z_y=-sin(x^5y^4)*4x^5y^3=-4x^5y^3sin(x^5y^4)$
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