Answer
$$f'\left( x \right) = 6{e^x} + x{e^x}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \left( {x + 5} \right){e^x} \cr
& {\text{Calculate the derivative of the function}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left( {\left( {x + 5} \right){e^x}} \right) \cr
& {\text{use the product rule }} \cr
& f'\left( x \right) = {e^x}\frac{d}{{dx}}\left( {x + 5} \right) + \left( {x + 5} \right)\frac{d}{{dx}}\left( {{e^x}} \right) \cr
& {\text{compute derivatives}} \cr
& f'\left( x \right) = {e^x}\left( 1 \right) + \left( {x + 5} \right){e^x} \cr
& {\text{multiply}} \cr
& f'\left( x \right) = {e^x} + x{e^x} + 5{e^x} \cr
& f'\left( x \right) = 6{e^x} + x{e^x} \cr} $$
