Differentiabilitet af vektorfunktionMan kan ikke se p\303\245 2D-banekurve for en vektorfunktion f(t)=(x(t),y(t)) om den er differentiabel.NB: Man skal unders\303\270ge om hver af koordinatfunktionerne x(t) og y(t) er differentiabel.Eksempel p\303\245 en differentiabel vektorfunktion af 2 variableLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ=Definer f\303\270lgende koordinat-funktioner:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2KFEieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1JKG1mZW5jZWRHRiQ2Jy1GIzYnLUYsNihRInRGJ0YvRjJGNEY3RjpGL0Y0L0Y4RjxGOkYvRjRGRUY6LUkjbW9HRiQ2MFEiPUYnRi9GNEZFRjovJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaLUZHNjBRInxmckYnRi9GNEZFRjovRktGMUZML0ZPRjFGUEZSRlRGVi9GWVEsMC4xNjY2NjY3ZW1GJy9GZm5GXW8tSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtRiM2Jy1JJW1zdXBHRiQ2JUZCLUYjNigtSSNtbkdGJDYnUSIyRidGL0Y0RkVGOkYvRjJGNEY3RjovJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRi9GNEZFRjovJSlyb3dhbGlnbkdRIUYnLyUsY29sdW1uYWxpZ25HRmhwLyUrZ3JvdXBhbGlnbkdGaHAvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGX3EtRmZvNigtRiM2Ky1GRzYwUSRmb3JGJ0YvRjRGRUY6RkpGTEZORlBGUkZURlYvRllRJjAuMGVtRicvRmZuRmpxLUZHNjBRIn5GJ0YvRjRGRUY6RkpGTEZORlBGUkZURlZGaXFGW3JGQi1GRzYwUSI+RidGL0Y0RkVGOkZKRkxGTkZQRlJGVEZWRlhGZW4tRmBwNidGZXBGL0Y0RkVGOkYvRjRGRUY6RmZwRmlwRltxRl1xRmBxRmZwRmlwRltxLUZjbzYnLUZmbzYoLUYjNidGYnJGL0Y0RkVGOkZmcEZpcEZbcUZdcUZgcS1GZm82KC1GIzYrRmZxRlxyRkItRkc2MFEmJmxlcTtGJ0YvRjRGRUY6RkpGTEZORlBGUkZURlZGWEZlbi1GLDYoRmVwRi9GMkY0RjdGOkYvRjRGRUY6RmZwRmlwRltxRl1xRmBxRmZwRmlwRltxLyUmYWxpZ25HUSVheGlzRicvRmdwUSliYXNlbGluZUYnL0ZqcFEnY2VudGVyRicvRlxxUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGMS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmB0LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRlt1LyUmZnJhbWVHRlt1LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGNi8lLWVxdWFsY29sdW1uc0dGNi8lLWRpc3BsYXlzdHlsZUdGNi8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZodC1GLDYjRmhwRi9GNEZFRjo= og 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i planen kn\303\246kker LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2J1EjOTBGJy8lJWJvbGRHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGOi1GIzYoLUkjbWlHRiQ2KFEib0YnRjIvJSdpdGFsaWNHRjRGNS9GOVEsYm9sZC1pdGFsaWNGJ0Y7RjJGQ0Y1RkVGOy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGNS9GOVEnbm9ybWFsRic= i (0,0):NB: Her er kun 2 kordinater: x og y.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 funktionen f(t)=(x(t),y(t)) er en differentiabel funktion, da koordinatfunktionerne x(t) og y(t) er differentiable: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Koordinatfunktionernes afledede x'(t) og y'(t) er kontinuerte funktioner af 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og 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i rummet er differentiabel:NB: Her er 3 kordinater: t, x og y.(Rot\303\251r grafen og se fra forskellige vinkler. Grafen er simpelthen glat - ogs\303\245 i 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)(Pr\303\270v ogs\303\245 at dreje koordinatsystemet, s\303\245 t-aksen g\303\245r ud af sk\303\246rmen samt x-aksen til h\303\270jre og y-aksen opad. S\303\245 fremkommer banekurven i x-y-planen.)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Eksempel p\303\245 en ikke-differentiabel vektorfunktion af 2 variableLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==QyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIiDefiner f\303\270lgende koordinat-funktioner: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 og 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QyU+SSJ4RzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMjkkIiIhLCRGMSMiIiIiIiMxRjJGMSwkRjFGNkYlRiVGJSEiIi8uLUYkRidGPA==QyU+SSJ5RzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMjkkIiIhLCRGMSMiIiIiIiMxRjJGMSwkRjFGNkYlRiVGJSEiIi8uLUYkRidGPA==Banekurven i planen er en ret linje:NB: Her er kun 2 kordinater: x og y.LUklcGxvdEc2IjYnNyUtSSJ4R0YkNiNJInRHRiQtSSJ5R0YkRikvRio7ISIlIiIiL0kmY29sb3JHRiRJJHJlZEdGJC9JKnRoaWNrbmVzc0dGJCIiJC9JJ2xhYmVsc0dGJDckRihGLC9JJ2xlZ2VuZEdGJDcjUTRiYW5la3VydmVufml+cGxhbmVuRiQ=Men koordinatfunktionerne x(t) og y(t) er ikke differentiable:(grafen kn\303\246kker i 0)LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYoLUkieEdGJzYjSSJ0R0YnL0YsOyEiIyIiIi9JJmNvbG9yR0YnSSVibHVlR0YnL0kqdGhpY2tuZXNzR0YnIiIkL0knbGFiZWxzR0YnNyRGLEYqL0knbGVnZW5kR0YnNyNRJXgodClGJw==LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYoLUkieUdGJzYjSSJ0R0YnL0YsOyEiIyIiIi9JJmNvbG9yR0YnSSVibHVlR0YnL0kqdGhpY2tuZXNzR0YnIiIkL0knbGFiZWxzR0YnNyRGLEYqL0knbGVnZW5kR0YnNyNRJXkodClGJw==Banekurven i rummet er ikke-differentiabel:NB: Her er 3 kordinater: t, x og y.(Rot\303\251r grafen og se fra forskellige vinkler. Grafen kn\303\246kker i 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)(Pr\303\270v ogs\303\245 at dreje koordinatsystemet, s\303\245 t-aksen g\303\245r ud af sk\303\246rmen samt x-aksen til h\303\270jre og y-aksen opad. S\303\245 fremkommer banekurven i x-y-planen.)LUkrc3BhY2VjdXJ2ZUc2IjYoNyUtSSJ4R0YkNiNJInRHRiQtSSJ5R0YkRilGKi9GKjshIiMiIiMvSSp0aGlja25lc3NHRiQiIiQvSSZjb2xvckdGJEkmYnJvd25HRiQvSSVheGVzR0YkSSZCT1hFREdGJC9JJ2xhYmVsc0dGJDclRihGLEYq