Question

if f(x)=x*e^(-2*x^2), then f'(x)=e^(-2*x^2), right?

Answer 1

No, I just made the same mistake as you a minute ago though lol
So, the rule for \[f'(x) = e ^{g(x)} \]
is \[g'(x)*e ^{g(x)}\]

Answer 2

So you'd have the derivative of the function e is being raised to times the original function. And don't forget the product rule since you have an x in there. See if you can do it from there =)