Calculate $\mathbf{r}'(t)$, $\mathbf{T}(t)$, and $\mathbf{T}(4)$ where $$\mathbf{r}(t)=\langle t^{2}, 3t^{4}\rangle.$$

$\mathbf{r}'(t) = \langle$ $,$ $\rangle$.
$\mathbf{T}(t) = \langle$ $,$ $\rangle$.
$\mathbf{T}(4) = \langle$ $,$ $\rangle$.