Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.3 - Partial Derivatives - 14.3 Exercise - Page 924: 22

Answer

$f_x=\frac{y-x}{(x+y)^3}$, $f_y=\frac{-2x}{(x+y)^3}$.

Work Step by Step

$f(x,y)=\frac{x}{(x+y)^2}$ In order to find $f_x$ we treat $y$ as a constant and differentiate with respect to $x$. $f_x=\frac{(x+y)^2-2x{(x+y)}}{(x+y)^4}=\frac{y-x}{(x+y)^3}$ In order to find $f_y$ we treat $x$ as a constant and differentiate with respect to $y$. $f_y=\frac{-2x}{(x+y)^3}$
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