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Something idk
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alexander
2025-12-15 20:19:09 +01:00
parent c7cf9d130e
commit 701b3ec932
1 changed files with 7 additions and 0 deletions
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src/Analysis_rewrite.typ
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@@ -248,6 +248,11 @@
- $f(x)$ ist an der Stelle $x_0 in DD$ diffbar wenn \ - $f(x)$ ist an der Stelle $x_0 in DD$ diffbar wenn \
#MathAlignLeft($ f'(x_0) = lim_(x->x_0 plus.minus) (f(x_0 + h - f(x_0))/h) $) #MathAlignLeft($ f'(x_0) = lim_(x->x_0 plus.minus) (f(x_0 + h - f(x_0))/h) $)
- $f(x)$ diffbar $=>$ $f(x)$ stetig - $f(x)$ diffbar $=>$ $f(x)$ stetig
- Tangente an $x_0$: $f(x_0) + f'(x_0)(x - x_0)$
- Beste #underline([linear]) Annäherung
- Tangente $t(x)$ von $f(x)$ an der Stelle $x_0$: $ lim_(x->0) (f(x) - f(x_0))/(x-x_0) -f'(x_0) =0 $
*Ableitung Regeln*
#grid( #grid(
row-gutter: 3mm, row-gutter: 3mm,
@@ -267,7 +272,9 @@
[$f(x) = c : f'(x) = 0$], [$f(x) = c : f'(x) = 0$],
[$c dot f(x) : c dot f'(x)$], [$c dot f(x) : c dot f'(x)$],
[$(x^(-n)) n in NN : n x^(n-1)$], [$(x^(-n)) n in NN : n x^(n-1)$],
[$e^(x) : e^(x)$],
) )
- Kettenregel: $f(g(x)) : f'(g(x)) dot g'(x)$
] ]
#colbreak() #colbreak()