Answer
$${\bf{r}}'\left( t \right) = \sin t{\bf{j}}$$
Work Step by Step
$$\eqalign{
& {\bf{r}}\left( t \right) = 4{\bf{i}} - \cos t{\bf{j}} \cr
& {\text{Differentiate}} \cr
& {\bf{r}}'\left( t \right) = \frac{d}{{dt}}\left[ {{\bf{r}}\left( t \right)} \right] \cr
& {\bf{r}}'\left( t \right) = \frac{d}{{dt}}\left[ {4{\bf{i}} - \cos t{\bf{j}}} \right] \cr
& {\bf{r}}'\left( t \right) = \frac{d}{{dt}}\left[ 4 \right]{\bf{i}} - \frac{d}{{dt}}\left[ {\cos t} \right]{\bf{j}} \cr
& {\bf{r}}'\left( t \right) = 0{\bf{i}} - \left( { - \sin t} \right){\bf{j}} \cr
& {\bf{r}}'\left( t \right) = \sin t{\bf{j}} \cr} $$
