Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 782: 70


$$ R_{uvw}= 2(v+w)^{-3}=\frac{2}{(v+w)^{3}}.$$

Work Step by Step

Since $ R(u,v,w)=\frac{u}{v+w}$, then we have $$ R_{u}=\frac{1}{v+w}=(v+w)^{-1},$$ $$ R_{uv}= -(v+w)^{-2},$$ $$ R_{uvw}= 2(v+w)^{-3}=\frac{2}{(v+w)^{3}}.$$
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