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Diketahui . Nilai  adalah ...

Pertanyaan

Diketahui straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x minus 2 over denominator straight x plus 5 end fraction. Nilai straight f apostrophe left parenthesis negative 4 right parenthesis adalah ...

  1. 17 

  2. 14 

  3. 13 

  4. 2 

  5. 1 

Pembahasan Soal:

Misal u dan v adalah fungsi yang mempunyai turunan, maka:

open parentheses straight u over straight v close parentheses to the power of apostrophe equals fraction numerator straight u apostrophe straight v minus uv apostrophe over denominator straight v squared end fraction

Pada soal, diketahui straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x minus 2 over denominator straight x plus 5 end fraction

misalkan:

  • straight u left parenthesis straight x right parenthesis equals 3 straight x minus 2 maka straight u apostrophe left parenthesis straight x right parenthesis equals 3 
  • straight v left parenthesis straight x right parenthesis equals straight x plus 5 maka straight v apostrophe left parenthesis straight x right parenthesis equals 1 

Turunan pertama dari fungsi straight f left parenthesis straight x right parenthesis equals fraction numerator 3 straight x minus 2 over denominator straight x plus 5 end fraction adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 3 open parentheses straight x plus 5 close parentheses minus 1 open parentheses 3 straight x minus 2 close parentheses over denominator open parentheses straight x plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 3 straight x plus 15 minus 3 straight x plus 2 over denominator open parentheses straight x plus 5 close parentheses squared end fraction end cell row blank equals cell 17 over open parentheses straight x plus 5 close parentheses squared end cell end table 

Nilai straight f apostrophe left parenthesis negative 4 right parenthesis yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f apostrophe left parenthesis negative 4 right parenthesis end cell equals cell 17 over open parentheses negative 4 plus 5 close parentheses squared end cell row blank equals cell 17 over 1 squared end cell row blank equals 17 end table 

Jadi, nilai straight f apostrophe left parenthesis negative 4 right parenthesis adalah 17.

Oleh karena itu, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Nuryani

Mahasiswa/Alumni Universitas Padjadjaran

Terakhir diupdate 02 Mei 2021

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Pertanyaan yang serupa

Turunan pertama dari adalah . Nilai

Pembahasan Soal:

u left parenthesis x right parenthesis equals left parenthesis 3 x plus 5 right parenthesis rightwards arrow u apostrophe left parenthesis x right parenthesis equals 3  v left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis rightwards arrow v apostrophe left parenthesis x right parenthesis equals 1 space m a k a  f left parenthesis x right parenthesis equals fraction numerator u left parenthesis x right parenthesis over denominator v left parenthesis x right parenthesis end fraction  f left parenthesis x right parenthesis equals fraction numerator u apostrophe left parenthesis x right parenthesis v left parenthesis x right parenthesis minus v apostrophe left parenthesis x right parenthesis u left parenthesis x right parenthesis over denominator v squared left parenthesis x right parenthesis end fraction  f left parenthesis x right parenthesis equals fraction numerator 3 left parenthesis x minus 2 right parenthesis minus left parenthesis 3 x plus 5 right parenthesis over denominator left parenthesis x minus 2 right parenthesis squared end fraction  f left parenthesis x right parenthesis equals fraction numerator negative 11 over denominator left parenthesis x minus 2 right parenthesis squared end fraction    K e m u d i a n  f apostrophe left parenthesis 1 right parenthesis equals fraction numerator negative 11 over denominator left parenthesis 1 minus 2 right parenthesis squared end fraction  f apostrophe left parenthesis 1 right parenthesis equals negative 11

0

Roboguru

Fungsi turunan dari .

Pembahasan Soal:

Turunan dari f open parentheses x close parentheses equals fraction numerator u open parentheses x close parentheses over denominator v open parentheses x close parentheses end fraction adalah:

f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe open parentheses x close parentheses v open parentheses x close parentheses minus u open parentheses x close parentheses v apostrophe open parentheses x close parentheses over denominator open parentheses v open parentheses x close parentheses close parentheses squared end fraction

Akan dicari turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction.

Misalkan :

table attributes columnalign right center left columnspacing 2px end attributes row cell u open parentheses x close parentheses end cell equals cell 3 x minus 5 end cell row cell v open parentheses x close parentheses end cell equals cell x minus 1 end cell end table

Sehingga diperoleh :

table attributes columnalign right center left columnspacing 2px end attributes row cell u apostrophe left parenthesis x right parenthesis end cell equals 3 row cell v apostrophe open parentheses x close parentheses end cell equals 1 end table

Turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction adalah :

table attributes columnalign right center left columnspacing 2px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u apostrophe open parentheses x close parentheses v open parentheses x close parentheses minus u open parentheses x close parentheses v apostrophe open parentheses x close parentheses over denominator open parentheses v open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 3 open parentheses x minus 1 close parentheses close parentheses minus open parentheses open parentheses 3 x minus 5 close parentheses 1 close parentheses over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 3 x minus 3 close parentheses minus open parentheses 3 x minus 5 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x minus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 3 x minus 3 x minus 3 plus 5 over denominator x squared minus 2 x plus 1 end fraction end cell row blank equals cell fraction numerator 2 over denominator x squared minus 2 x plus 1 end fraction end cell end table

Jadi, fungsi turunan dari f open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator x minus 1 end fraction adalah fraction numerator 2 over denominator x squared minus 2 x plus 1 end fraction.

0

Roboguru

Jika  dan , maka  = ....

Pembahasan Soal:

0

Roboguru

Diketahui dengan a bilangan bulat. Jika , nilai a adalah...?

Pembahasan Soal:

Diketahui:

f open parentheses x close parentheses equals fraction numerator 2 x minus 1 over denominator a x minus 1 end fraction

f apostrophe left parenthesis 1 right parenthesis equals 1 fourth

Ditanyakan:

a equals... ?

Penyelesaian:

Pertama kita menentukan turunan pertama fungsi f open parentheses x close parentheses: dengan rumus:

f left parenthesis x right parenthesis equals fraction numerator g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction comma space maka space f apostrophe left parenthesis x right parenthesis equals fraction numerator g left parenthesis x right parenthesis apostrophe times h left parenthesis x right parenthesis minus g left parenthesis x right parenthesis times h left parenthesis x right parenthesis apostrophe over denominator open parentheses h left parenthesis x right parenthesis close parentheses squared end fraction

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 open parentheses a x minus 1 close parentheses minus open parentheses open parentheses 2 x minus 1 close parentheses a close parentheses over denominator open parentheses a x minus 1 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 a x minus 2 minus open parentheses 2 a x minus a close parentheses over denominator a squared x squared minus 2 a x plus 1 end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative 2 plus a over denominator a squared x squared minus 2 a x plus 1 end fraction end cell end table

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative 2 plus a over denominator a squared x squared minus 2 a x plus 1 end fraction end cell row cell f apostrophe open parentheses 1 close parentheses end cell equals cell fraction numerator negative 2 plus a over denominator a squared open parentheses 1 close parentheses squared minus 2 a open parentheses 1 close parentheses plus 1 end fraction end cell row cell 1 fourth end cell equals cell fraction numerator negative 2 plus a over denominator a squared minus 2 a plus 1 end fraction end cell row cell a squared minus 2 a plus 1 end cell equals cell negative 8 plus 4 a end cell row cell a squared minus 2 a plus 1 plus 8 minus 4 a end cell equals 0 row cell a squared minus 6 a plus 9 end cell equals 0 row cell open parentheses a minus 3 close parentheses left parenthesis a minus 3 right parenthesis end cell equals 0 row a equals 3 end table

Sehingga nilai a adalah 3.

Jadi, jawaban yang tepat adalah B

 

 

0

Roboguru

Diketahui fungsi dan f'(x) merupakan turunan pertama dari f(x). Hasil dari f'(x) = .....

Pembahasan Soal:

I n g a t space r u m u s  f open parentheses x close parentheses equals u over v  M a k a  f to the power of apostrophe open parentheses x close parentheses equals fraction numerator u to the power of apostrophe v minus u v apostrophe over denominator v squared end fraction  J a d i  f open parentheses x close parentheses equals fraction numerator 2 x minus 5 over denominator 3 x plus 1 end fraction  f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 2 open parentheses 3 x plus 1 close parentheses minus open parentheses 2 x minus 5 close parentheses 3 over denominator open parentheses 3 x plus 1 close parentheses squared end fraction  f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 6 x plus 2 minus 6 x plus 15 over denominator open parentheses 3 x plus 1 close parentheses squared end fraction  f to the power of apostrophe open parentheses x close parentheses equals 17 over open parentheses 3 x plus 1 close parentheses squared

0

Roboguru

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