University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.3 - Partial Derivatives - Exercises - Page 702: 29


$f_x=\dfrac{1}{x+2y+3z} ; \\ f_y= \dfrac{2}{x+2y+3z} ; \\ f_z=\dfrac{3}{x+2y+3z}$

Work Step by Step

Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by keeping $y$ and $z$ as a constant, and vice versa: $f_x=\dfrac{1}{x+2y+3z} ; \\ f_y=(2) \times \dfrac{1}{x+2y+3z}=\dfrac{2}{x+2y+3z} ; \\ f_z=(3) \times \dfrac{1}{x+2y+3z}=\dfrac{3}{x+2y+3z}$
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