I must be doing something wrong here.

I would factor it out with a u sub:
y=u+2

So... y'=u = x^2-3x?

Wolfram was no help to me at all. ._.[url=http://www.wolframalpha.com/input/?i=derivative+of+%28x%5E2-3x%2B2%29+with+respect+to+%28x%5E2-3x%29][/url]

Uhh..failure.
If y=u+2, then dy/du=1. Not u.
Lol, why you need Wolfram for such an easy problem?

If you're differentiating wrt something other than x, then you treat that as the new variable.
d/d(x^2-3x)(x^2-3x+2) = 1.