Answer
$$h'\left( x \right) = - 2{e^{ - 2x}}$$
Work Step by Step
$$\eqalign{
& h\left( x \right) = {e^{ - 2x}} - {e^2} \cr
& {\text{Calculate the derivative of the function}} \cr
& h'\left( x \right) = \frac{d}{{dx}}\left( {{e^{ - 2x}} - {e^2}} \right) \cr
& h'\left( x \right) = \frac{d}{{dx}}\left( {{e^{ - 2x}}} \right) - \frac{d}{{dx}}\left( {{e^2}} \right) \cr
& {\text{Compute derivatives}}{\text{, use }}\frac{d}{{dx}}\left( {{e^u}} \right) = {e^u}\frac{{du}}{{dx}},{\text{ }}{e^2}{\text{ is a constant its derivative is 0}} \cr
& h'\left( x \right) = {e^{ - 2x}}\frac{d}{{dx}}\left( { - 2x} \right) - 0 \cr
& h'\left( x \right) = {e^{ - 2x}}\left( { - 2} \right) \cr
& h'\left( x \right) = - 2{e^{ - 2x}} \cr} $$
