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: 25


$$ z_x= \frac{2x}{x^2+y^2} , \quad z_y= \frac{2y}{x^2+y^2} . $$

Work Step by Step

Recall that $(\ln x)'=\dfrac{1}{x}$ Since $ z=\ln(x^2+y^2)$, then by using the chain rule, we have $$ z_x= \frac{2x}{x^2+y^2} , \quad z_y= \frac{2y}{x^2+y^2} . $$
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