Answer
$$ F_{rst}=0.$$
Work Step by Step
Since $ F(r,s,t)=r(s^2+t^2)$, then we have
$$ F_{r}= s^2+t^2,\quad F_{rs}=2s .$$
Then, we have
$$ F_{rst}=0.$$
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: 67
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