Answer
$\textbf{r}'(1) = \langle 1, 6, 3\rangle$
Work Step by Step
$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$
$\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$
$\textbf{r}(t) = \langle t,3t^2,t^3\rangle$
$\textbf{r}'(t) = \langle 1, 6t, 3t^2\rangle$
$\textbf{r}'(1) = \langle 1, 6(1), 3(1)^2\rangle = \langle 1, 6, 3\rangle$