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: 9


$$ r'(s)=\left\langle 3 e^{3s},-e^{-s}, 4s^{3} \right \rangle .$$

Work Step by Step

Since $ r(s)=\langle e^{3s},e^{-s}, s^{4} \rangle $ then, by using the chain rule, the derivative $ r'(s)$ is given by $$ r'(s)=\left\langle (3s)' e^{3s},-e^{-s}, 4s^{3} \right \rangle =\left\langle 3e^{3s},-e^{-s}, 4s^{3} \right \rangle.$$
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