Answer
$$ R_{uvw}= 2(v+w)^{-3}=\frac{2}{(v+w)^{3}}.$$
Work Step by Step
Since $ R(u,v,w)=\frac{u}{v+w}$, then we have
$$ R_{u}=\frac{1}{v+w}=(v+w)^{-1},$$
$$ R_{uv}= -(v+w)^{-2},$$
$$ R_{uvw}= 2(v+w)^{-3}=\frac{2}{(v+w)^{3}}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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