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I. Differentiation – 2. Partielle afledede 36 d 1 (ln(x)) = dx x d dx (ax ) = ln(a)a x 2.4. Botanik for afledte ☞ [S] 3.1, 3.4 Derivatives. . . d (sin(x)) = cos(x) dx d (cos(x)) = −sin(x) dx d dx (tan(x)) = 1 + tan2 (x) d dx (sin−1 1 (x)) = √ 1 − x2 d dx (tan−1 (x)) = 1 1 + x2
I. Differentiation – 2. Partielle afledede 37 2.5. Vælg og afled ☞ [S] 11.3 Partial derivatives Eksempel 1 Givet funktionen f(x,y) = x 3 + x 2 y 3 − 2y 2 Hold y fast Hold x fast d dx f(x,y) = 3x2 + 2xy 3 d dy f(x,y) = 3x2 y 2 − 4y 2.6. Partielt afledt ☞ [S] 11.3 Partial derivatives 4 Definition Den partielle afledede af f(x,y) med hensyn til x i punktet (a,b) er ∂f f(a + h,b) − f(a,b) (a,b) = lim ∂x h→0 h Den partielle afledede af f(x,y) med hensyn til y i punktet (a,b) er ∂f f(a,b + h) − f(a,b) (a,b) = lim ∂y h→0 h
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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