Answer
$$5$$
Work Step by Step
$$\eqalign{
& {\left. {\frac{d}{{dx}}\left[ {f\left( x \right) + g\left( x \right)} \right]} \right|_{x = 1}} \cr
& {\text{Calculate the derivative}} \cr
& \frac{d}{{dx}}\left[ {f\left( x \right) + g\left( x \right)} \right] = f'\left( x \right) + g'\left( x \right) \cr
& {\text{Evaluate at }}x = 1 \cr
& {\left. {\frac{d}{{dx}}\left[ {f\left( x \right) + g\left( x \right)} \right]} \right|_{x = 1}} = f'\left( 1 \right) + g'\left( 1 \right) \cr
& {\text{From the table we know that }}f'\left( 1 \right) = 3{\text{ and }}g'\left( 1 \right) = 2 \cr
& {\left. {\frac{d}{{dx}}\left[ {f\left( x \right) + g\left( x \right)} \right]} \right|_{x = 1}} = 3 + 2 \cr
& {\left. {\frac{d}{{dx}}\left[ {f\left( x \right) + g\left( x \right)} \right]} \right|_{x = 1}} = 5 \cr} $$
