# Derivative

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DERIVATIVE. Coming from another; taken from something preceding, secondary; as derivative title, which is that acquired from another person. There is considerable difference between an original and a derivative title. When the acquisition is original, the right thus acquired to the thing becomes property, which must be unqualified and unlimited, and since no one but the occupant has any right to the thing, he must have the whole right of disposing of it. But with regard to derivative acquisition, it may be otherwise, for the person from whom the thing is acquired may not have an unlimited right to it, or he may convey or transfer it with certain reservations of right. Derivative title must always be by contract.
2. Derivative conveyances are, those which presuppose some other precedent conveyance, and serve only to enlarge, confirm, alter, restrain, restore, or transfer the interest granted by such original conveyance, 3 Bl. Com. 321.

A Law Dictionary, Adapted to the Constitution and Laws of the United States. By John Bouvier. Published 1856.
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where [g.sub.n](z) is the ordinary derivative of g(z) of order n (n [member of] N0 := N U {0}), being tacitly assumed (forsimplicity) that g(z) is the polynomial part (if any) of the product f(z)g(z).
(the latter for m [member of] N = {1, 2, 3, ...}), For c = 0 one writes (1A) [sub.0][D.sup.[alpha].sub.z][f(z)] = [D.sup.[alpha].sub.z][f(z)] as in the classical RL operator of order [alpha] (or -[alpha]), Moreover when c [right arrow] [infinity] (1.1) may be identified with the familiar Weyl fractional derivative (or integral) of order [alpha] (or -[alpha]), An ordinary derivative corresponds to [alpha] = 1 with (1B) (d/dz)[f(z)] = [D.sup.[alpha].sub.z][f(z)], The binomial Leibnitz rule for derivatives is
The concept of the first-order ordinary derivative is as old as calculus, says Mukhopadhyay, who is identified only be name, but higher order derivatives are particularly interesting because they can exist without the first-order derivative existing.

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