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: 38


$$ w_x= \frac{1}{y+z} ,\quad w_y= -x(y+z)^{-2},\quad w_z=-x(y+z)^{-2}. $$

Work Step by Step

Recall that $(x^n)'=nx^{n-1}$ Since $ w=\frac{x}{y+z}=x(y+z)^{-1}$, we have $$ w_x= \frac{1}{y+z} ,\quad w_y= -x(y+z)^{-2},\quad w_z=-x(y+z)^{-2}. $$
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