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I. Differentiation – 5. Gradient 103
5.26. Retningsafledt, 3 variable ☞ [S] 11.6 Directional derivatives and the . . .
Eksempel 5
Gradienten af f(x,y,z) = xsin yz er
∇f = (sin yz,xz cos yz,xy cos yz)
For den retningsafledede i retning (1,2, −1) bruges enhedsvektoren
u = 1
√ 6 (1,2, −1)
Duf = (sin yz,xz cos yz,xy cos yz) · 1 √ 6 (1,2, −1)
= 1 √ 6 (sin yz + 2xz cos yz − xy cos yz)
5.27. Retningsafledt, 3 variable ☞ [S] 11.6 Directional derivatives and the . . .
Eksempel 5 - fortsat
I retning u = 1
√ 6 (1,2, −1) er
I punktet (x,y,z) = (1,3,0) fås
Duf = (sin yz,xz cos yz,xy cos yz) · 1 √ 6 (1,2, −1)
Duf(1,3,0) = (0,0,3) · 1 √ 6 (1,2, −1)