Question

find derivative of f(x)=e^-x^2 /2

Answer 1

Remember that \[e^{u} = u'e^{u}\] which is a chain rule.
Therefore, for this one, \[u = -\frac{ x ^{2} }{ 2 }\] so the derivative of u: \[x' = -x\]
Hence, \[f'(x) = -xe^{ -\frac{ x ^{2} }{ 2 }}\]