#### Answer

$$ - 20x{e^{ - 10{x^2}}}$$

#### Work Step by Step

$$\eqalign{
& \frac{d}{{dx}}\left( {{e^{ - 10{x^2}}}} \right) \cr
& {\text{by }}\frac{d}{{dx}}\left( {{e^{u\left( x \right)}}} \right) = {e^{u\left( x \right)}}u'\left( x \right) \cr
& = {e^{ - 10{x^2}}}\frac{d}{{dx}}\left( { - 10{x^2}} \right) \cr
& = {e^{ - 10{x^2}}}\left( { - 20x} \right) \cr
& {\text{simplify}} \cr
& = - 20x{e^{ - 10{x^2}}} \cr} $$