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I. Differentiation – 4. Kædereglen 70 Ved symmetri Differentialet er 4. Kædereglen wy = y x2 + y2 + z2 ,wz z = x2 + y2 + z2 dw = xdx + ydy + zdz x 2 + y 2 + z 2 4.1. Oversigt ☞ [S] 3.5, 11.5 Nøgleord og begreber ✌ Kædereglen i en variabel ✌ Kædereglen to variable ✌ Test kædereglen ✌ Kædereglen i tre eller flere variable ✌ Jacobimatricen ✌ Kædereglen på matrixform ✌ Test matrixform ✌ Differentiation af implicit funktion
I. Differentiation – 4. Kædereglen 71 ✌ Test implicit funktion 4.2. Sammensat funktion ☞ [S] 3.5 The chain rule Sætning (Kædereglen) For f(u), u = g(x) differentiable er den sammensatte funktion F = f ◦ g differentiabel med For y = F(x) = f(g(x)) skrives F ′ (x) = f ′ (g(x))g ′ (x) dy dy du = dx du dx 4.3. Overbevis ☞ [S] 3.5 The chain rule Bevis ∆u = g(x + ∆x) − g(x), ∆y = f(u + ∆u) − f(u) giver der har kædereglen som grænseværdi for ∆x → 0. ∆y ∆y ∆u = ∆x ∆u ∆x dy dy du = dx du dx 4.4. Brug kæderegel ☞ [S] 3.5 The chain rule
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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I. Differentiation - 1. Kontinuitet
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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1. Vektorer og matricer V Matricer
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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