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7/23/2019 DIFERENSIASI FUNGSI
http://slidepdf.com/reader/full/diferensiasi-fungsi 1/18
DIFERENSIA SI FUNGSI
OLEH :
NUR ADIN RAHSANJANI
14509134017
B2
7/23/2019 DIFERENSIASI FUNGSI
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A. PENGERTIAN DAN NOTASI
DIFERENSIASI FUNGSI :
7/23/2019 DIFERENSIASI FUNGSI
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Diferensiasi = Derivatif =
Turunan. Turunan suatu fungsi f (X)adalah f ’ (X) yang harganya
dapat dicari dengan rumus :f ( X !" # f (X"
f $ (X" % L&'&
! 0 !
7/23/2019 DIFERENSIASI FUNGSI
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= !menyatakan turunannya
adalah :"Turunan pertama terhadap Xditulis :
"Turunan kedua terhadap Xditulis :
"Turunan ketiga terhadap X
ditulis :
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B. RU)US*RU)US DASAR TURUNAN FUNGSI
ALJABAR :
+,-/, -,,,/ R' /'//,/ -/,/ f/& /,/
'6 &'& -8 ',,&',/,/ -'*-' ,,-,,& -& :
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J&, 8 / ,,,! &,/,/R, ;A ,/ B % f/&*f/& X "
= # ’ = $
= #X ’ = #
= Xn
’ = nXn%&
= k Xn ’ = k.nXn%&
= ' ’ = '’ ’
= ' * ’ = '’ * ’
= ' . ’ = '’. ’ '.’
= ’ =
7/23/2019 DIFERENSIASI FUNGSI
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. RU)US TURUNAN FUNGSI TRIGONO)ETRI
7/23/2019 DIFERENSIASI FUNGSI
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= sin X
= c+s X = tg X
= c+tg X
= sec X
= c+sec X
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D. RU)US TURUNAN IN<ERS FUNGSITRIGONO)ETRI
7/23/2019 DIFERENSIASI FUNGSI
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= arc. sin X = arc. c+s X
= arc. tg X
7/23/2019 DIFERENSIASI FUNGSI
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,. RU)US TURUNAN FUNGSI HIPERBOLI+
7/23/2019 DIFERENSIASI FUNGSI
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= sinh X = c+sh X = tgh X
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F. RU)US TURUNAN IN<ERSFUNGSI HIPERBOLI+
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= arc. sinh X = arc. c+sh X
= arc. tgh X
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G. RU)US TURUNAN FUNGSI E+SPONENSIAL
7/23/2019 DIFERENSIASI FUNGSI
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= e- ’ = e-
= ef (-) ’ = f (X) . ef (X)
= a- ’ = a- . ln a = af (-) ’ = f (X) . af
(X) . ln a
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H. RU)US TURUNAN FUNGSI LOGARIT)A
7/23/2019 DIFERENSIASI FUNGSI
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= l+g a-
dy f / ( X ) = l+g af (X) %
• d- f (X) . ln a
= ln X
= ln f (X)