Calculus (3rd Edition)

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

Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 8

Answer

$$ r'(t)=\left\langle -1,\frac{2}{\sqrt{t}},0\right \rangle.$$

Work Step by Step

Since $ r(t)=\langle 7-t,4\sqrt{t}, 8 \rangle $, then the derivative $ r'(t)$ is given by $$ r'(t)=\left\langle -1,\frac{4}{2\sqrt{t}},0\right \rangle =\left\langle -1,\frac{2}{\sqrt{t}},0\right \rangle.$$
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