What does derivated mean?
In the context of calculus, I think it means differentiated...
Given a function
#f'(x) = lim_(h->0)(f(x+h)-f(x))/h#
The resulting function
In other fields (e.g. chemistry) one product that has been derived from another may be called a derivate. By a common (American?) practice, nouns often turn into verbs, so instead of derive, you might say derivate, meaning to make something into a derivate.
If so, then derivated is the past participle of to derivate, i.e. it means derived.
So in the context of calculus derivated probably means the same as differentiated. That is: derived by a process of differentiation.
Personally I prefer differentiated, but perhaps the apparently synthetic word derivated may be helpful in order to distinguish it from other uses of differentiated or of derived.