# 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.

References in periodicals archive ?
We say that the function f: [OMEGA] [right arrow] Y is H-differentiable (differentiable in the sense of Hadamard) at the point a [member of] [OMEGA] if there exists u [member of] L(X,Y) such that
(2) the functions [[phi].sub.1[sigma]] and [[phi].sub.2[sigma]] are two differentiable functions and [[[D.sup.1.sub.2][phi](x)].sup.[sigma]] = [[[phi]'.sub.2[sigma]](x), [[phi]'.sub.1[sigma]](x)], when [phi] is (2)-differentiable.
f is first-order differentiable, so in convex domain D, first-order difference of f can be written in the following integral form:
Let J be a differentiable application on [[OMEGA].sub.0].
Recently, Farid [3] extended Theorems 1 and 2 to functions of two variables that are differentiable on their coordinates.
For nonnegative and differentiable functions i, [m.sub.0], and [m.sub.1]: [[a.sub.0], [omega]] [right arrow] R, with [DELTA]m(a) = [m.sub.1](a)-[m.sub.0] (a) [greater than or equal to] 0 for all a [member of] [[a.sub.0], [omega]], the system of ODEs given by equations (1) and (2) with initial conditions S([a.sub.0]) = [S.sub.0] [greater than or equal to] 0, C([a.sub.0]) = [C.sub.0] [greater than or equal to] 0, and S([a.sub.0])+ C([a.sub.0]) > 0 has a unique solution S and C with N(a) = S(a) + C(a) [greater than or equal to] 0 for all a [member of] [[a.sub.0], [omega]].
If f (x) is differentiable at x = a then it is continuous at x = a.
there exists a twice continuously differentiable function v :
Let X be a real Banach space, and let [PHI], [PSI] : X [right arrow] R be two continuously Gateaux differentiable functionals such that [inf.sub.X] [PHI] = [PHI](0) = [PSI](0) = 0.
As an application of the main results, it is shown that if we identify every fuzzy number with the corresponding equivalence class, there would be more differentiable fuzzy functions than what is found in the literature.
Motivated by the above works, in this paper we give some applications and examples for trapezoidal and midpoint type inequalities when the intended function is differentiable. Furthermore we consider integral quadrature formula and give an error estimate related to trapezoidal and midpoint formula.
The main disadvantage can be seen immediately by considering (7): the terminal condition [PSI] must be infinitely Malliavin differentiable. In contradistinction, the viscosity solution given in [7] necessitates [PSI] to be only bounded and continuous.

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