# differential quotient

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## derivative

[dih-riv-uh-tiv]

- derived.
- not original; secondary.

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- something that has been derived.
- Also called derived form. Grammar. a form that has undergone derivation from another, as atomic from atom.
- Chemistry. a substance or compound obtained from, or regarded as derived from, another substance or compound.
- Also called differential quotient; especially British, differential coefficient. Mathematics. the limit of the ratio of the increment of a function to the increment of a variable in it, as the latter tends to 0; the instantaneous change of one quantity with respect to another, as velocity, which is the instantaneous change of distance with respect to time.Compare first derivative, second derivative.
- a financial contract whose value derives from the value of underlying stocks, bonds, currencies, commodities, etc.

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## Origin of derivative^{}

1400–50; late Middle English derivatif < Late Latin dērīvātīvus, equivalent to Latin dērīvāt(us) (see derivation) + -īvus -ive

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## derivative

- resulting from derivation; derived
- based on or making use of other sources; not original or primary
- copied from others, esp slavishly; plagiaristic

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- a term, idea, etc, that is based on or derived from another in the same class
- a word derived from another word
- chem a compound that is formed from, or can be regarded as formed from, a structurally related compoundchloroform is a derivative of methane
- maths
- Also called: differential coefficient, first derivativethe change of a function, f(x), with respect to an infinitesimally small change in the independent variable, x; the limit of [f(a + Δ x)–f(a)] / Δ x, at x = a, as the increment, Δ x, tends to 0. Symbols: df(x)/d x, f′(x), Df(x)the derivative of x n is nx n–1
- the rate of change of one quantity with respect to anothervelocity is the derivative of distance with respect to time

- finance a financial instrument, such as a futures contract or option, the price of which is largely determined by the commodity, currency, share price, interest rate, etc, to which it is linked
- psychoanal an activity that represents the expression of hidden impulses and desires by channelling them into socially acceptable forms

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Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History for differential-quotient

## derivative

early 15c. (adj.); mid-15c. (n.), from Middle French dérivatif (15c.), from Late Latin derivat-, past participle stem of Latin derivare (see derive). Mathematical sense is from 1670s.

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Online Etymology Dictionary, © 2010 Douglas Harper

## derivative

(dĭ-rĭv′ə-tĭv)- Something obtained or produced by modification of something else.
- A chemical compound that may be produced from another compound of similar structure in one or more steps.

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- Resulting from, characterized by, or employing derivation.

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The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.

## derivative

[dĭ-rĭv′ə-tĭv]

- In calculus, the slope of the tangent line to a curve at a particular point on the curve. Since a curve represents a function, its derivative can also be thought of as the rate of change of the corresponding function at the given point. Derivatives are computed using differentiation.

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The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.