Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 21


$f_{R_1}=-R_1^{-2}$ $f_{R_2}=-R_2^{-2}$ $f_{R_3}=-R_3^{-2}$

Work Step by Step

Rewrite the equation: $f(R_1, R_2, R_3)=R_1^{-1}+R_2^{-1}+R_3^{-1}$ Take the first partial derivatives of the given function. When taking partial derivative with respect to $R_1$, treat $R_2$ and $R_3$ as constants. Use this same method when taking partial derivative with respect to $R_2$ and $R_3$: $f_{R_1}=-R_1^{-2}+0+0=-R_1^{-2}$ $f_{R_2}=0-R_2^{-2}+0=-R_2^{-2}$ $f_{R_3}=0+0-R_3^{-2}=-R_3^{-2}$
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