derivative

Etymology

From Middle French dérivatif, from Latin dērīvātus, perfect passive participle of dērīvō (“I derive”). Related with derive; By surface analysis, derive + -ative.

adj

1. Obtained by derivation; not radical, original, or fundamental.
   a derivative conveyance
   a derivative word
   People started talking about the pandemic as if it were itself a television show; as the second wave hit last fall, they griped about the derivative writing on Covid Season 2. 2021-04-27, Amanda Hess, “Inject the Vaccine Fan Fiction Directly Into My Veins”, in The New York Times, →ISSN
2. Imitative of the work of someone else.
   No, I really felt it was very derivative. To me it it looked like it was straight out of Diane Arbus, but it had none of the wit. 1979, Woody Allen, Manhattan, spoken by Mary (Diane Keaton)
3. (law">law, copyright law">law) Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.
4. (finance) Having a value that depends on an underlying asset of variable value.

noun

1. Something derived.
2. (linguistics) A word that derives from another one.
   Coordinate term: cognate
3. (finance) A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
4. (chemistry) A chemical derived from another.
5. (calculus) One of the two fundamental objects of study in calculus (the other being integration), which quantifies the rate of change, tangency, and other qualities arising from the local behavior of a function.
   1. (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 Leibniz's notation, ̇f(x) in Newton's notation (the latter used particularly when the independent variable is time).
      The derivative of x² is 2x; if f(x)=x², then f'(x)=2x
   2. 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.
      The derivative of f(x)=x³ at x=2 is 12.
   3. (Of more general classes of functions) Any of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.
   4. (generally) The linear operator that maps functions to their derived functions, usually written D; the simplest differential operator.