Question

derivative xe^((-x^2)/2)

Answer 1

chain rule plus product rule.
\[(fg)'=f'g+g'f\] with
\[f(x)=x,f'(x)=1,g(x)=e^{-\frac{x^2}{2}},g'(x)=-xe^{-\frac{x^2}{2}}\]

Answer 2

\[ xe ^{-x ^{2}/2}\]

\[(1-x ^{2})\times e ^{-x ^{2}/x}\]

Answer 3

that "x" in the middle is multiplication