Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Preliminary Questions - Page 780: 1



Work Step by Step

The mistake is to differentiate $ y^2$ with respect to $ x $ as $2y $. The correct formula is $$\frac{\partial }{\partial x}(x^2y^2)=\frac{\partial x^2}{\partial x}y^2+\frac{\partial y^2}{\partial x}x^2=2xy^2+0=2xy^2.$$
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