#### Answer

$\textbf{r}'(t) = \langle e^{-t}-te^{-t}, ln(t) + 1, cos(t) - t\ sin(t)\rangle$

#### Work Step by Step

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$
$\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$
$\textbf{r}(t) = \langle te^{-t}, t\ ln(t), t\ cos(t)\rangle$
Using Product Rule:
$\textbf{r}'(t) = \langle e^{-t}-te^{-t}, ln(t) + 1, cos(t) - t\ sin(t)\rangle$