"difference quotient" meaning in English

See difference quotient in All languages combined, or Wiktionary

Noun

Forms: difference quotients [plural]
Head templates: {{en-noun}} difference quotient (plural difference quotients)
  1. (mathematical analysis) A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations:
    (calculus) 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.
    Related terms: derivative, difference equation Translations (difference quotient): cociente diferencial [masculine] (Asturian), quocient de diferències [masculine] (Catalan), 差商 (chāshāng) (Chinese Mandarin), differenskvotient [common-gender] (Danish), differentiaalquotiënt [neuter] (Dutch), erotusosamäärä (Finnish), quotient des différences [masculine] (French), quotient des variations [masculine] (French), cociente da diferenza [masculine] (Galician), Differenzenquotient [masculine] (German), rapporto incrementale [masculine] (Italian), quociente de diferenças [masculine] (Portuguese), cociente incremental [masculine] (Spanish), cociente de diferencias [masculine] (Spanish)
    Sense id: en-difference_quotient-en-noun-Y6j-7wq1 Categories (other): Calculus, Mathematical analysis Topics: calculus, mathematical-analysis, mathematics, sciences Disambiguation of 'difference quotient': 61 39
  2. (mathematical analysis) A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations:
    (geometry) 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.
    Sense id: en-difference_quotient-en-noun-CFTEigJX Categories (other): Geometry, Mathematical analysis, English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Asturian translations, Terms with Catalan translations, Terms with Danish translations, Terms with Dutch translations, Terms with Finnish translations, Terms with French translations, Terms with Galician translations, Terms with German translations, Terms with Italian translations, Terms with Mandarin translations, Terms with Portuguese translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 31 69 Disambiguation of Entries with translation boxes: 33 67 Disambiguation of Pages with 1 entry: 28 72 Disambiguation of Pages with entries: 28 72 Disambiguation of Terms with Asturian translations: 32 68 Disambiguation of Terms with Catalan translations: 32 68 Disambiguation of Terms with Danish translations: 30 70 Disambiguation of Terms with Dutch translations: 33 67 Disambiguation of Terms with Finnish translations: 35 65 Disambiguation of Terms with French translations: 25 75 Disambiguation of Terms with Galician translations: 32 68 Disambiguation of Terms with German translations: 32 68 Disambiguation of Terms with Italian translations: 32 68 Disambiguation of Terms with Mandarin translations: 31 69 Disambiguation of Terms with Portuguese translations: 30 70 Disambiguation of Terms with Spanish translations: 25 75 Topics: geometry, mathematical-analysis, mathematics, sciences

Inflected forms

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        "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."
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        "(mathematical analysis) A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations:",
        "(calculus) 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."
      ],
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          "_dis1": "61 39",
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          "_dis1": "61 39",
          "code": "ast",
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          "sense": "difference quotient",
          "tags": [
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          "word": "cociente diferencial"
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          "code": "ca",
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          "sense": "difference quotient",
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          "word": "quocient de diferències"
        },
        {
          "_dis1": "61 39",
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "chāshāng",
          "sense": "difference quotient",
          "word": "差商"
        },
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          "_dis1": "61 39",
          "code": "da",
          "lang": "Danish",
          "sense": "difference quotient",
          "tags": [
            "common-gender"
          ],
          "word": "differenskvotient"
        },
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          "_dis1": "61 39",
          "code": "nl",
          "lang": "Dutch",
          "sense": "difference quotient",
          "tags": [
            "neuter"
          ],
          "word": "differentiaalquotiënt"
        },
        {
          "_dis1": "61 39",
          "code": "fi",
          "lang": "Finnish",
          "sense": "difference quotient",
          "word": "erotusosamäärä"
        },
        {
          "_dis1": "61 39",
          "code": "fr",
          "lang": "French",
          "sense": "difference quotient",
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        },
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          "_dis1": "61 39",
          "code": "fr",
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          "sense": "difference quotient",
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          "word": "quotient des variations"
        },
        {
          "_dis1": "61 39",
          "code": "gl",
          "lang": "Galician",
          "sense": "difference quotient",
          "tags": [
            "masculine"
          ],
          "word": "cociente da diferenza"
        },
        {
          "_dis1": "61 39",
          "code": "de",
          "lang": "German",
          "sense": "difference quotient",
          "tags": [
            "masculine"
          ],
          "word": "Differenzenquotient"
        },
        {
          "_dis1": "61 39",
          "code": "it",
          "lang": "Italian",
          "sense": "difference quotient",
          "tags": [
            "masculine"
          ],
          "word": "rapporto incrementale"
        },
        {
          "_dis1": "61 39",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "difference quotient",
          "tags": [
            "masculine"
          ],
          "word": "quociente de diferenças"
        },
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          "_dis1": "61 39",
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          "sense": "difference quotient",
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          "word": "cociente incremental"
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          "_dis1": "61 39",
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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 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."
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          "tangent line",
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        "(mathematical analysis) A mathematical quantity of the form (f(a+h)-f(a))/h for some function f(x), having two main interpretations:",
        "(geometry) 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."
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  "word": "difference quotient"
}
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        "(calculus) 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."
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        "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."
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    {
      "code": "ast",
      "lang": "Asturian",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "cociente diferencial"
    },
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "quocient de diferències"
    },
    {
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      "lang": "Chinese Mandarin",
      "roman": "chāshāng",
      "sense": "difference quotient",
      "word": "差商"
    },
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      "code": "da",
      "lang": "Danish",
      "sense": "difference quotient",
      "tags": [
        "common-gender"
      ],
      "word": "differenskvotient"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "difference quotient",
      "tags": [
        "neuter"
      ],
      "word": "differentiaalquotiënt"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "difference quotient",
      "word": "erotusosamäärä"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "quotient des différences"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "quotient des variations"
    },
    {
      "code": "gl",
      "lang": "Galician",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "cociente da diferenza"
    },
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      "code": "de",
      "lang": "German",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "Differenzenquotient"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "rapporto incrementale"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "quociente de diferenças"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "cociente incremental"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "difference quotient",
      "tags": [
        "masculine"
      ],
      "word": "cociente de diferencias"
    }
  ],
  "wikipedia": [
    "en:difference quotient"
  ],
  "word": "difference quotient"
}

Download raw JSONL data for difference quotient meaning in English (5.0kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-06-24 from the enwiktionary dump dated 2025-06-20 using wiktextract (074e7de and f1c2b61). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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