## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 38

#### Answer

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

#### 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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