Answer
$\textbf{r}''(t) = \langle 396t^{10}-2, 56t^6 + 6t, 20t^{-6}\rangle$
$\textbf{r}'''(t) = \langle 3960t^9, 336t^5+6, -120t^{-7}\rangle$
Work Step by Step
To find the derivative, simply find the derivative of each component.
$\textbf{r}(t) = \langle 3t^{12}-t^2, t^8+t^3, t^{-4}-2\rangle$
$\textbf{r}'(t) = \langle 36t^{11}-2t, 8t^7+3t^2, -4t^{-5}\rangle$
$\textbf{r}''(t) = \langle 396t^{10}-2, 56t^6 + 6t, 20t^{-6}\rangle$
$\textbf{r}'''(t) = \langle 3960t^9, 336t^5+6, -120t^{-7}\rangle$
