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Differentialregning

Differentialregning. Differentiation af simple funktioner og regneregler. Definitioner. Definition. f er kontinuert i x 0 . Definition f er differentiabel i x 0 . =. Definition f er differentiabel i x 0 . =. Tangentligning: y = f ’(x 0 )  (x – x 0 ) + f(x 0 ). f(x)=x 2.

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Differentialregning

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  1. Differentialregning Differentiation af simple funktioner og regneregler

  2. Definitioner Definition f er kontinuert i x0 Definition f er differentiabel i x0  =

  3. Definition f er differentiabel i x0  = Tangentligning: y = f ’(x0)(x – x0) + f(x0) f(x)=x2 (x0+h , f(x0+h)) f(x0+h) Δy h f(x0) x0

  4. (kf)'(x) (f + g)'(x) (f - g)'(x) (f  g)'(x) Regneregler

  5. Bevis for (kf)'(x) =

  6. Bevis for

  7. Bevis for (fg)'(x)

  8. Bevis for Fortsættes

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