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A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations:
The average rate of change of the function f(x) over the interval [a,,a+h]. As h approaches zero, the value of (f(a+h)-f(a))/h approaches the derivative or instantaneous rate of change of f(x) at x=a.
Definition source: English Wiktionary via Wiktextract
Topics: calculus, mathematical-analysis, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations:
The slope of the secant line passing through the points (a,,f(a)) and (a+h,,f(a+h)). As the horizontal distance h>0 between the points approaches zero, the slope of this secant line approaches the slope of the tangent line to f(x) at x=a, which is equal to the derivative of f(x) at x=a.
Definition source: English Wiktionary via Wiktextract
Topics: geometry, mathematical-analysis, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
14 source translations are retained for this English entry.
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Asturian:
cociente diferencial
— difference quotient
-
Catalan:
quocient de diferències
— difference quotient
-
Chinese Mandarin:
差商
(chāshāng)
— difference quotient
-
Danish:
differenskvotient
— difference quotient
-
Dutch:
differentiaalquotiënt
— difference quotient
-
Finnish:
erotusosamäärä
— difference quotient
-
French:
quotient des différences
— difference quotient
-
French:
quotient des variations
— difference quotient
-
Galician:
cociente da diferenza
— difference quotient
-
German:
Differenzenquotient
— difference quotient
-
Italian:
rapporto incrementale
— difference quotient
-
Portuguese:
quociente de diferenças
— difference quotient
-
Spanish:
cociente incremental
— difference quotient
-
Spanish:
cociente de diferencias
— difference quotient
