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KalkulusAturan-aturan Diferensial

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leibniz'snotation

f'(x)

Dxf(x)

dydx

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theoremA

Dx(k)= 0

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theoremB

Dx(x)= 1

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theoremC

Dx(xn

)= nxn-1

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theoremC

Dx(x-

n)= -nx-n-

1

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theoremD

Dx[k.f(x)] = k.Dx[f(x)]

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theoremE

Dx[f(x) + g(x)]= Dxf(x) + Dxg(x)

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theoremF

Dx[f(x) - g(x)]= Dxf(x) - Dxg(x)

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theoremG

Dx[f(x)g(x)]= Dxf(x) . Dxg(x)

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theoremG

Dx[f(x)g(x)]= f(x)Dxg(x)+g(x)Dxf(x)

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f(x) = (x2 + 2)(x3 + 1)

f'(x) =?

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theoremHDx[f(x) /

g(x)]g(x)Dxf(x) – f(x)Dxg(x)

g2(x)=

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f(x) = 3

f'(x) =?x3

1x4–

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KalkulusDiferensial Trigonometri

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Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id 17 of

sin x < x < tan x

Untuk tiap0 < x < π/2

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tan x < x < sin x

Untuk tiap-π/2 < x < 0

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sin x < x < tan xsin x sin x sin x

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1 < x < 1sin x cos x

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limx 0

= 11

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limx 0

1cos x

= 1

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limx 0

xsin x

= 1

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limx 0

sin xx

= 1

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limx 0

1-cos xx

= 0

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theoremA

Dx(sin x)

= cos x

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theoremB

Dx(cos x)

= -sin x

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nexttheorem

Dx(sec x)

= sec x tan

x

Dx(tan x)

= sec2x

Dx(cotan x)

= -cosec2xDx(cosec x) = -cosec x

cotan x

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”“

GottfriedLeibniz

Finally there are simple ideas of which no definition can be given; there are also

axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof

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GottfriedLeibniz

Monad