derivative

Etymology

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

Pronunciation

• (UK) IPA^(key): /dɪˈɹɪvətɪv/

• Audio (US):

  (file)

Adjective

derivative (comparative more derivative, superlative most derivative)

1. Obtained by derivation; not radical, original, or fundamental.

   a derivative conveyance

   a derivative word

   • 2021 April 27, Amanda Hess, “Inject the Vaccine Fan Fiction Directly Into My Veins”, in The New York Times‎, →ISSN:

     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.

2. Imitative of the work of someone else.
   • 1979, Woody Allen, Manhattan, spoken by Mary (Diane Keaton):

     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.

3. (law, copyright 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

derivative (plural derivatives)

1. Something derived.
2. (linguistics) A word that derives from another one.

   Synonyms: descendant, formative, reflex

   Antonyms: ancestor, etymon, root

   Hyponym: 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.
6. (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 ${\displaystyle f(x)}$) The derived function of ${\displaystyle f(x)}$: the function giving the instantaneous rate of change of ${\displaystyle f}$; equivalently, the function giving the slope of the line tangent to the graph of ${\displaystyle f}$. Written ${\displaystyle f'(x)}$ or ${\displaystyle {\frac {df}{dx}}}$ in Leibniz's notation, ${\displaystyle {\dot {f}}(x)}$ in Newton's notation (the latter used particularly when the independent variable is time).

      The derivative of ${\displaystyle x^{2}}$ is ${\displaystyle 2x}$; if ${\displaystyle f(x)=x^{2}}$, then ${\displaystyle f'(x)=2x}$

   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 ${\displaystyle f(x)=x^{3}}$ at ${\displaystyle x=2}$ is ${\displaystyle 12}$.

   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 ${\displaystyle D}$; the simplest differential operator.

Pronunciation

• Audio:

  (file)

Adjective

derivative

1. inflection of derivativ:
   1. strong/mixed nominative/accusative feminine singular
   2. strong nominative/accusative plural
   3. weak nominative all-gender singular
   4. weak accusative feminine/neuter singular

Adjective

derivative

1. feminine plural of derivativo

Adjective

dērīvātīve

1. vocative masculine singular of dērīvātīvus