Answer
$$ z_x=4x^3y+y^{-2},\quad z_y=x^4-2xy^{-3}.$$
Work Step by Step
Recall that $(x^n)'=nx^{n-1}$
Since $ z=x^4y+xy^{-2}$, then we have
$$ z_x=4x^3y+y^{-2},\quad z_y=x^4-2xy^{-3}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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