type derivation for 'map map', yelp

*newbie alert* I'm hoping this is a permissible question to ask here. I looked at the FAQ and it doesn't seem to explicitly disallow it. :)

I was learning haskell a few years ago and I was recommended mr. Hudak's book "The Haskell School of Expression". This was my first foray into functional programming and it turned out this wasn't a great book to start with. Having done some amount of Haskelling by now I regret to realize that when I see an expression like "map map" I continue to scratch my head. Hudak gives this and similar examples as exercises, but there are no solutions in the back of the book.

The funny thing is that I've written map map to map a function over items in lists contained in a list. But I still don't understand this at all:
map map :: [a -> b] -> [[a] -> [b]]
Let alone how you derive it.