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: 33


$w_x=\frac{1}{x+2y+3z}$, $w_y=\frac{2}{x+2y+3z}$, $w_z=\frac{3}{x+2y+3z}$.

Work Step by Step

$w=\ln{(x+2y+3z)}$ In order to find $w_x$ we treat $y$ and $z$ as constants and differentiate with respect to $x$. $w_x=\frac{1}{x+2y+3z}$ Analogously. $w_y=\frac{2}{x+2y+3z}$ $w_z=\frac{3}{x+2y+3z}$
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