Answer
$\mathrm{r}^{\prime}(t)=\langle \sec^{2}t,\quad \sec t\tan t, \displaystyle \quad \frac{-2}{t^{3}} \rangle$
Work Step by Step
Parametric equations: $\mathrm{r}(t):\quad\left\{\begin{array}{ll}
x=\tan t & \\
y=\sec t & \\
y=t^{-2} &
\end{array}\right.$
Differentiate $(\displaystyle \frac{d}{dt})$ each component function
$\mathrm{r}^{\prime}(t):\quad\left\{\begin{array}{l}
x=\sec^{2}t\\
y=\sec t\tan t\\
z=-2t^{-3}
\end{array}\right.$
$\mathrm{r}^{\prime}(t)=\langle \sec^{2}t,\quad \sec t\tan t, \displaystyle \quad \frac{-2}{t^{3}} \rangle$
