Etymology is not destiny, as we keep pointing out here. Thinking that it is is subscribing to the Etymological Fallacy (see here, among many other places). But even synchronically, you can't always trust what you see: derived lexical items are often specialized semantically (as are noun-noun compounds and also combinations of non-predicating adjective plus noun). This is especially true of technical terms; as I am fond of saying: labels are not definitions.
Which brings us to financial derivatives. Derivative here is derived from derive, right? So we can tell what it means in this expression from its morphological composition, right? Well, no. But people want that to be true.
So we get this letter to the New York Times (19 October, Week in Review, p. 11):
The financial industry's quant formulas are not beyond the layman's understanding.
"Derivatives" may sound familiar from high school calculus; they are functions whose value is derived from the value of another, known function.
That's true as far as it goes. But it is utterly uninformative. It tells us nothing about the meaning of derivative in financial contexts. Or, in fact, about derivative in calculus. The label is appropriate, but it's far from a definition.
(For the record, the derivative f'(x) of a function f(x) in calculus is the function that provides the value of the rate of change of f(x). It's a very specific kind of "derivative". Financial derivatives have nothing in particular to do with rates of change.)