Find the derivative of y=xe^-x^2.

Is the x being multiplied by (e^-x^2)?
Product rule?
I don't understand how to approach this problem.

yes, the product rule, and also the chain rule:

y = (x)(e^-x^2)
y' = (1)(e^-x^2) + (x)(e^-x^2)(-2x)
= (1-2x^2)e^-x^2

If y = e^u, then
y' = e^u u'