@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q1503239 rdfs:label "مبرهنة شفارز"@ar,
        "Teorema de Clairaut-Schwartz"@ca,
        "Clairauts sætning"@da,
        "Satz von Schwarz"@de,
        "symmetry of second derivatives"@en,
        "simetrio de duaj derivoj"@eo,
        "teorema de Clairaut"@es,
        "théorème de Schwarz"@fr,
        "Simetri turunan kedua"@id,
        "teorema di Schwarz"@it,
        "ヤングの定理"@ja,
        "이계 도함수의 대칭성"@ko,
        "ဒုတိယ ဆင်းသက်ချက်များ၏ အချိုးညီမှု"@my,
        "symmetry of second derivatives"@nl,
        "Twierdzenie Schwarza"@pl,
        "teorema de Clairaut-Schwarz"@pt,
        "teorema de Schwarz"@pt-br,
        "Simetria derivatei a doua"@ro,
        "Равенство смешанных производных"@ru,
        "Schwarzov izrek"@sl,
        "Рівність змішаних похідних"@uk,
        "二阶导数的对称性"@zh,
        "二阶导数的对称性"@zh-hans,
        "二階導數的對稱性"@zh-hant,
        "二階導數的對稱性"@zh-hk ;
    schema1:dateModified "2026-09-07T10:47:22+00:00"^^xsd:dateTime ;
    schema1:description "مبرهنة في التحليل الرياضي"@ar,
        "teorema matemàtic"@ca,
        "mathematischer Satz"@de,
        "theorem"@en,
        "teorema de cálculo diferencial"@es,
        "théorème d'analyse"@fr,
        "teorema matematico"@it,
        "twierdzenie rachunku różniczkowego"@pl,
        "matematični izrek"@sl ;
    schema1:version 2541643034 ;
    wikibase:identifiers 6 ;
    wikibase:sitelinks 17 ;
    wikibase:statements 14 ;
    skos:altLabel "مبرهنة كليرو"@ar,
        "مبرهنة كليرو-شفارز"@ar,
        "مبرهنة يونغ"@ar,
        "simetria de les segones derivades"@ca,
        "teorema de Schwartz"@ca,
        "teorema de Young"@ca,
        "Clairaut's theorem"@en,
        "Schwarz's theorem"@en,
        "Young's theorem"@en,
        "teoremo de Schwarz"@eo,
        "teorema de Schwartz"@es,
        "égalité de Schwarz"@fr,
        "teorema di Schwartz"@it,
        "Twierdzenie Clairaut"@pl,
        "teorema de Clairault"@pt,
        "teorema de Clairault-Schwarz"@pt,
        "teorema de Clairaut"@pt,
        "teorema de Schwarz"@pt,
        "teorema de Clairaut"@pt-br,
        "teorema de Clairaut-Schwarz-Young"@pt-br,
        "teorema de Young"@pt-br,
        "Teorema lui Clairaut"@ro,
        "Teorema lui Schwarz"@ro,
        "Теорема Шварца"@ru,
        "Clairautov izrek"@sl,
        "Youngov izrek"@sl,
        "Рівність мішаних похідних"@uk ;
    p:P11497 wds:Q1503239-604F6185-39A2-4313-A7CB-7F007AC879A7 ;
    p:P12385 wds:Q1503239-afd21849-3e96-47b6-9999-d1be4d93c81f ;
    p:P1296 wds:Q1503239-0CE24A2F-9558-461D-86C9-EEF2416366A8 ;
    p:P138 wds:Q1503239-26f6f77f-424c-4770-2d7e-4ec8c92fd758,
        wds:Q1503239-762ee01b-4eff-8bd8-41f3-211cf1409bc7,
        wds:Q1503239-f3863437-40cc-659f-35d6-962a36a347bb ;
    p:P1889 wds:Q1503239-8ed7d45d-46d4-c814-0f38-0e3623cad99c ;
    p:P2534 wds:Q1503239-a511a884-4923-c02a-db9c-9a613b4c7b15 ;
    p:P2579 wds:Q1503239-2F84AD8F-2105-4D70-9B5B-9089AD0ABC97 ;
    p:P31 wds:Q1503239-A8E703B0-82D4-4C93-920A-F9C0BBFBC8D1 ;
    p:P6104 wds:Q1503239-D5811E12-A2C2-4210-9F05-61320D984243 ;
    p:P6366 wds:Q1503239-AFAF7073-6CB6-40E3-90BC-15ED395913BA ;
    p:P646 wds:Q1503239-EB6CA1E1-A8C1-40E4-AEE0-12D5C96050AD ;
    p:P7554 wds:Q1503239-82F69954-AC59-47C5-9B85-D7187F87C593 ;
    wdtn:P6366 <https://makg.org/entity/2780778300> ;
    wdt:P11497 "1.5.E6" ;
    wdt:P12385 "teorema-de-schwarz" ;
    wdt:P1296 "0061472" ;
    wdt:P138 wd:Q28937,
        wd:Q61223,
        wd:Q869557 ;
    wdt:P1889 wd:Q1068385 ;
    wdt:P2534 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(</mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi><mi>y</mi></mrow></mrow></mfrac></mrow><mi>f</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy=\"false\">)</mo><mo data-mjx-texclass=\"CLOSE\">)</mo></mrow><mo stretchy=\"false\">=</mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi><mi>y</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(</mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>&#x2202;</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mi>f</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy=\"false\">)</mo><mo data-mjx-texclass=\"CLOSE\">)</mo></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P2579 wd:Q149972 ;
    wdt:P31 wd:Q65943 ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "2780778300" ;
    wdt:P646 "/m/0256q9" ;
    wdt:P7554 "Partial_derivative" .

