Answer
$\quad-(2 \ln 2)(3 \mathrm{i}-\mathrm{j}+\mathrm{k})$
Work Step by Step
We find:
\[
\begin{array}{l}
\mathrm{r}_{1}^{\prime}(t)=(-\ln 2) e^{t \ln 2} \mathrm{r}^{\prime}\left(2-e^{t \ln 2}\right) \\
\qquad \begin{array}{l}
\mathrm{r}_{1}^{\prime}(1)=-(2 \ln 2) \mathrm{r}^{\prime}(0) \\
=-(2 \ln 2)(3 \mathrm{i}-\mathrm{j}+\mathrm{k}) \\
\end{array}
\end{array}
\]
