Answer
$\textbf{r}''(t) = \langle -9cos(3t), -16sin(4t), -36cos(6t)\rangle$
$\textbf{r}'''(t) = \langle 27sin(3t), -64cos(4t), 216sin(6t)\rangle$
Work Step by Step
To find the derivative, simply find the derivative of each component.
$\textbf{r}(t) = \langle cos(3t), sin(4t), cos(6t)\rangle$
$\textbf{r}'(t) = \langle -3sin(3t), 4cos(4t), -6sin(6t)\rangle$
$\textbf{r}''(t) = \langle -9cos(3t), -16sin(4t), -36cos(6t)\rangle$
$\textbf{r}'''(t) = \langle 27sin(3t), -64cos(4t), 216sin(6t)\rangle$
