Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 814: 13

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

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