Formula for Var(XY)

The variance of two random variables, X+Y is in the beginning of every statistics book. The distribution of X/Y is a standard Cauchy variable. So when I tried to find the variance of X*Y, I figured no problem. But it is actually very difficult to find on the web, and tedious to derive. As a public service, here is the result when X and Y are both normally distributed:

Let V(x) and V(y) be the variance of X and Y respectively
Let C(x,y) be the covariance of X and Y

then the variance of the product XY, is

V(xy)=[E(x)]^2*V(y)+[E(y)]^2*V(x)+2*E(x)*E(y)*C(x,y)
+V(x)*V(y)+C(x,y)^2

note: see derivation from anonymous commenter (I can't get math in html for my blog, so God bless him)