derivative

Something derived.

(linguistics) A word that derives from another one.

(finance) A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.

(chemistry) A chemical derived from another.

(Of a function of a single variable f(x)) The derived function of f(x): the function giving the instantaneous rate of change of f; equivalently, the function giving the slope of the line tangent to the graph of f. Written f'(x) or (df)/(dx) in Leibnitz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time).

The value of such a derived function for a given value of its independent variable: the rate of change of a function at a point in its domain.

(Of more general classes of functions) Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.

(generally) The linear operator that maps functions to their derived functions, usually written D; the simplest differential operator.