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Herleitung der Ableitungsfunktion für sin(x)
\n`f(x) = sin(x)` .. Differentialquotient .. `\\display\\lim_(h->0) (f(x+h)-f(x))/h`
\n`\\display\\= lim_(h->0) (sin(x+h)-sin(x))/h`
\n`\\display\\= lim_(h->0) (sin(x)·cos(h)+cos(x)·sin(h)-sin(x))/h`
\n`\\display\\= lim_(h->0) (sin(x)(cos(h)-1)+cos(x)·sin(h))/h`
\n`\\display\\= lim_(h->0) (sin(x)(cos(h)-1))/h + lim_(h->0) (cos(x)·sin(h))/h`
\n`\\display\\= sin(x) · lim_(h->0) ((cos(h)-1))/h + cos(x) · lim_(h->0) sin(h)/h`
\n`\\display\\= sin(x) · 0 + cos(x) · 1`
\n`= cos(x)`
\n`=> f’(x) = cos(x)`\n","summary":"Ableitung der Trigonometrischen Funktionen","attachments":[{"tag":"","name":"sin cos Ableitung","file":"sin cos Ableitung.svg","mime":"image/svg+xml","type":"file","href":"data/Mathematik/Ableitungsregeln/Sinus%20und%20Cosinus%20ableiten/sin%20cos%20Ableitung.svg"},{"tag":"","name":"Ableitung trigonometrische","file":"Ableitung trigonometrische.svg","mime":"image/svg+xml","type":"file","href":"data/Mathematik/Ableitungsregeln/Sinus%20und%20Cosinus%20ableiten/Ableitung%20trigonometrische.svg"}],"subject":"Mathematik","modified":1679431037817,"author":"Holger Engels","links":"","keywords":"Herleitung, Differentialquotient","thumb":"sin cos Ableitung.svg","educationalLevel":"10,11,12","typicalAgeRange":"15-17","educationalContext":"Sekundarstufe I, Sekundarstufe II","sgs":"38002","created":1584745200000,"skills":[],"_attachments":{"Ableitung trigonometrische.svg":{"content_type":"image/svg+xml","revpos":4,"digest":"md5-jUonCKc6f6xFMq0cbyq4WQ==","length":22417,"stub":true},"sin cos Ableitung.svg":{"content_type":"image/svg+xml","revpos":3,"digest":"md5-f7A2Cz0prp+baYucQTvAEA==","length":15886,"stub":true}}}