Answer
$$f'\left( x \right) = 2{e^x} - 2x{e^x} - {x^2}{e^x}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = 2{e^x} - {x^2}{e^x} \cr
& {\text{Differentiate}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {2{e^x} - {x^2}{e^x}} \right] \cr
& f'\left( x \right) = 2\frac{d}{{dx}}\left[ {{e^x}} \right] - \underbrace {\frac{d}{{dx}}\left[ {{x^2}{e^x}} \right]}_{{\text{Product rule}}} \cr
& f'\left( x \right) = 2{e^x} - {e^x}\frac{d}{{dx}}\left[ {{x^2}} \right] - {x^2}\frac{d}{{dx}}\left[ {{e^x}} \right] \cr
& f'\left( x \right) = 2{e^x} - {e^x}\left( {2x} \right) - {x^2}\left( {{e^x}} \right) \cr
& {\text{Simplifying}} \cr
& f'\left( x \right) = 2{e^x} - 2x{e^x} - {x^2}{e^x} \cr} $$
