Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises - Page 481: 51

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

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