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Turunan fungsi dari adalah

Pertanyaan

Turunan fungsi dari f left parenthesis x right parenthesis equals fraction numerator x squared plus 4 x plus 4 over denominator 2 x minus 4 end fraction spaceadalah ....

Pembahasan Soal:

Diketahui fungsi f left parenthesis x right parenthesis equals fraction numerator x squared plus 4 x plus 4 over denominator 2 x minus 4 end fraction. Misalkan u equals x squared plus 4 x plus 4 space text dan end text space u apostrophe equals 2 x plus 4 x comma dan  v equals 2 x minus 4 space text dan end text space v apostrophe equals 2 comma maka turunan pertama dari fungsi f left parenthesis x right parenthesis equals fraction numerator x squared plus 4 x plus 4 over denominator 2 x minus 4 end fraction spaceyaitu

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 u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator open parentheses 2 x plus 4 close parentheses open parentheses 2 x minus 4 close parentheses minus 2 open parentheses x squared plus 4 x plus 4 close parentheses over denominator open parentheses 2 x minus 4 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 4 x squared minus 16 minus 2 x squared minus 8 x minus 8 over denominator open parentheses 2 x minus 4 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 x squared minus 8 x minus 24 over denominator 4 x squared minus 16 x plus 16 end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator x squared minus 4 x minus 12 over denominator 2 x squared minus 8 x plus 8 end fraction end cell end table


Jadi Turunan fungsi dari f left parenthesis x right parenthesis equals fraction numerator x squared plus 4 x plus 4 over denominator 2 x minus 4 end fraction spaceadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus 4 x minus 12 over denominator 2 x squared minus 8 x plus 8 end fraction. end cell end table

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Turunan pertama dari

Pembahasan Soal:

Misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 3 x squared rightwards double arrow u apostrophe equals 6 x end cell row v equals cell x minus 1 rightwards double arrow v apostrophe equals 1 end cell end table end style 

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses 6 x close parentheses open parentheses x minus 1 close parentheses minus open parentheses 1 close parentheses open parentheses 3 x squared close parentheses over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 6 x squared minus 6 x minus 3 x squared over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 3 x squared minus 6 x over denominator open parentheses x minus 1 close parentheses squared end fraction end cell end table end style 

Dengan demikian, turunan pertama dari fungsi tersebut adalah y=(x1)23x26x.

Roboguru

Diketahui fungsi . Nilai  adalah

Pembahasan Soal:

Dengan menggunakan penfaktoran diperoleh

begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator x squared minus 4 x minus 45 over denominator x plus 5 end fraction equals fraction numerator left parenthesis x plus 5 right parenthesis left parenthesis x minus 9 right parenthesis over denominator x plus 5 end fraction equals x minus 9 end style 

begin mathsize 14px style g open parentheses 1 close parentheses equals 1 minus 9 equals negative 8 end style 

Dengan menggunakan sifat begin mathsize 14px style f open parentheses x close parentheses equals c rightwards arrow f apostrophe open parentheses x close parentheses equals 0 end style dan begin mathsize 14px style f open parentheses x close parentheses equals c x blank rightwards arrow f apostrophe open parentheses x close parentheses equals c end style 

begin mathsize 14px style g open parentheses x close parentheses equals x minus 9 g apostrophe open parentheses x close parentheses equals 1 g " left parenthesis x right parenthesis equals 0  end style 

begin mathsize 14px style g " left parenthesis 5 right parenthesis equals 0 end style

    begin mathsize 14px style g open parentheses 1 close parentheses plus 5 g " left parenthesis 5 right parenthesis equals negative 8 plus 5 left parenthesis 0 right parenthesis equals negative 8 end style 

Jadi, nilai begin mathsize 14px style g open parentheses 1 close parentheses plus 5 g " left parenthesis 5 right parenthesis end style adalah begin mathsize 14px style negative 8 end style             undefined 

Roboguru

Turunan dari  adalah ....

Pembahasan Soal:

Apabila suatu fungsi bentuknya adalah begin mathsize 14px style y equals u over v end style, maka begin mathsize 14px style y apostrophe equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end style.

Suatu fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 5 over denominator 2 x plus 3 end fraction end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x plus 5 end cell row cell u apostrophe end cell equals 1 row v equals cell 2 x plus 3 end cell row cell v apostrophe end cell equals 2 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses apostrophe end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator 1 times open parentheses 2 x plus 3 close parentheses minus open parentheses x plus 5 close parentheses times 2 over denominator open parentheses 2 x plus 3 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x plus 3 minus open parentheses 2 x plus 10 close parentheses over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 x end strike plus 3 minus up diagonal strike 2 x end strike minus 10 over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction end cell row blank equals cell fraction numerator negative 7 over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction end cell end table end style  

Jadi, jawaban yang tepat adalah E.

Roboguru

Turunan pertama  adalah ..

Pembahasan Soal:

Perhatikan perhitungan berikut.

Ingat, turunan pada pembagian dua fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator p open parentheses x close parentheses over denominator q open parentheses x close parentheses end fraction equals u over v rightwards arrow f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell end table

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared end cell row cell u apostrophe end cell equals cell 2 x end cell end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row v equals cell 2 x plus 1 end cell row cell v apostrophe end cell equals 2 end table

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 u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator 2 x open parentheses 2 x plus 1 close parentheses minus 2 open parentheses x squared close parentheses over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 4 x squared plus 2 x minus 2 x squared over denominator 4 x squared plus 4 x plus 1 end fraction end cell row blank equals cell fraction numerator 2 x squared plus 2 x over denominator 4 x squared plus 4 x plus 1 end fraction end cell end table

Jadi, turunan pertama dari f open parentheses x close parentheses equals fraction numerator x squared over denominator 2 x plus 1 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 2 x over denominator 4 x squared plus 4 x plus 1 end fraction end cell end table.

Roboguru

1. Tentukan turunan pertama  dari fungsi berikut! a.

Pembahasan Soal:

Perhatikan penghitungan berikut!

 begin mathsize 14px style y equals 1 over open parentheses 3 x squared plus x minus 1 close parentheses squared y equals open parentheses 3 x squared plus x minus 1 close parentheses to the power of negative 2 end exponent fraction numerator d y over denominator d x end fraction equals negative 2 open parentheses 3 x squared plus x minus 1 close parentheses to the power of negative 2 minus 1 space end exponent open parentheses 2 times 3 x plus 1 minus 0 close parentheses fraction numerator d y over denominator d x end fraction equals negative 2 open parentheses 3 x squared plus x minus 1 close parentheses to the power of negative 3 space end exponent open parentheses 6 x plus 1 close parentheses fraction numerator d y over denominator d x end fraction equals fraction numerator negative 2 open parentheses 6 x plus 1 close parentheses over denominator open parentheses 3 x squared plus x minus 1 close parentheses to the power of 3 space end exponent end fraction fraction numerator d y over denominator d x end fraction equals fraction numerator negative 12 x minus 2 over denominator open parentheses 3 x squared plus x minus 1 close parentheses to the power of 3 space end exponent end fraction space end style    

Jadi, turunan pertama dari fungsi tersebut adalah begin mathsize 14px style fraction numerator d y over denominator d x end fraction equals fraction numerator negative 12 x minus 2 over denominator open parentheses 3 x squared plus x minus 1 close parentheses to the power of 3 space end exponent end fraction space end style .   

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