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