Answer
$$9$$
Work Step by Step
$$\eqalign{
& {\text{Calculate the derivative }}\frac{d}{{dx}}\left[ {xf\left( x \right)} \right]{\text{ using the product rule}} \cr
& \frac{d}{{dx}}\left[ {xf\left( x \right)} \right] = \left( 1 \right)f\left( x \right) + xf'\left( x \right) \cr
& \frac{d}{{dx}}\left[ {xf\left( x \right)} \right] = f\left( x \right) + xf'\left( x \right) \cr
& {\text{Calculate the derivative at }}x = 3 \cr
& {\left. {\frac{d}{{dx}}\left[ {xf\left( x \right)} \right]} \right|_{x = 3}} = f\left( 3 \right) + 3f'\left( 3 \right) \cr
& {\text{From the table we know that }}f\left( 3 \right) = 3{\text{ and }}f'\left( 3 \right) = 2 \cr
& {\left. {\frac{d}{{dx}}\left[ {xf\left( x \right)} \right]} \right|_{x = 3}} = 3 + 3\left( 2 \right) \cr
& {\left. {\frac{d}{{dx}}\left[ {xf\left( x \right)} \right]} \right|_{x = 3}} = 9 \cr} $$
