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 - Exercises - Page 781: 15


$$ z_x=4x^3y+y^{-2},\quad z_y=x^4-2xy^{-3}.$$

Work Step by Step

Recall that $(x^n)'=nx^{n-1}$ Since $ z=x^4y+xy^{-2}$, then we have $$ z_x=4x^3y+y^{-2},\quad z_y=x^4-2xy^{-3}.$$
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