Ito Process

Hi all,

I am stuck trying to understand a worked example relating to Ito
process. In the example, it asked to find the Ito representation of
Z(t) = X(t)Y(t) given X(t) = exp(W(t)-t/2) and Y(t) = (W(t)^2)-t

The example then goes on with the following:
dX(t) = X(t)dW(t)
dY(t) = 2W(t)dW(t)
d(X(t)Y(t)) = X(t)dY(t) + Y(t)dX(t) + 2X(t)W(t)dt = ....

OK, I've no problem with d(X(t)Y(t)) as it comes from the chain rule
for Ito process, but I can't figure out how to obtain dX(t) and dY(t).

Neither X(t) or Y(t) is in the form that has dt or dW(t) or int[...]ds
or int[...]dW(s). So, I'm not sure how I could use Ito's
representation of X(t) = X(0) + int[a(s)]ds + int[b(s)]dW(s). I assume
if X(t) or Y(t) is in that form, then I could use that representation
to identify a(s) and b(s), and use that in the equation below to work
out dX(t) & dY(t)

dg(t,X(t)) = [gt' + a(t)gx' + ((b(t)^2)/2)*gx'']dt + [b(t)gx']dW(t)

Any help is appreciated. Thanks.
.