torsdag den 11. juni 2015

Differentialkvotienter


Web-matematik

(k)’ = 0

(x)’ = 1


(ax + b) = a


(x2)’ = 2x


(x3)’ = 3x2


1x )’ =  − 1x2


(x)’ = 12x

(ax)’ = a⋅ ln(a)


Differentialregning (9)

(ex)’ = ex

(ekx) = ⋅ ekx


ln(x) = 1x


Differentialregning (8)

log’(x) = 1⋅ ln(10)

Differentialregning (12)

(xa)’ = ⋅ xa − 1

(xx)’ = x⋅ (ln(x) + 1)

Differentialregning (13)















1f (x) )’ =  − ’ (x)(x) ⇒


1x )’ =  − 1x2



1. Bevis:

1x )’ = x0x )’x0 − 11 )’ − x−21 =

− x−2 ⋅ x21 ⋅ x2 = − x−2 + 2x2 = − x0x2 = − 1x2


2. Bevis:

(1) = ⋅ 1x )’ =
(x)’ ⋅ 1x + ⋅ 1x )’ =


1 ⋅ 1x + ⋅ 1x )’ = 0

1x )’ =  −1xx =  − 1x2



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