Answer
$$7.5$$
Work Step by Step
$$\eqalign{
& {\left. {\frac{d}{{dx}}\left[ {1.5f\left( x \right)} \right]} \right|_{x = 2}} \cr
& {\text{Calculate the derivative}} \cr
& \frac{d}{{dx}}\left[ {1.5f\left( x \right)} \right] = 1.5f'\left( x \right) \cr
& {\text{Evaluate at }}x = 2 \cr
& {\left. {\frac{d}{{dx}}\left[ {1.5f\left( x \right)} \right]} \right|_{x = 2}} = 1.5f'\left( 2 \right) \cr
& {\text{From the table we know that }}f'\left( 2 \right) = 5 \cr
& {\left. {\frac{d}{{dx}}\left[ {1.5f\left( x \right)} \right]} \right|_{x = 2}} = 1.5\left( 5 \right) \cr
& {\left. {\frac{d}{{dx}}\left[ {1.5f\left( x \right)} \right]} \right|_{x = 2}} = 7.5 \cr} $$
