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Tentukan turunan pertama fungsi-fungsi berikut!

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 20 x minus 2 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half end style 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

turunan pertama dari fungsi tersebut adalah begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator negative 16 over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end style.

Pembahasan

Misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight u equals cell 20 x minus 12 end cell row straight v equals cell 2 x minus 1 end cell end table end style 

Ingat konsep turunan:

begin mathsize 14px style table row cell f open parentheses x close parentheses equals a x to the power of n end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals a times n x to the power of n minus 1 end exponent end cell row cell f open parentheses x close parentheses equals a end cell rightwards arrow cell f apostrophe open parentheses x close parentheses equals 0 end cell end table end style  

Maka diperoleh:

begin mathsize 14px style table row cell straight u equals 20 x minus 2 end cell rightwards arrow cell straight u apostrophe equals 20 end cell row cell straight v equals 2 x minus 1 end cell rightwards arrow cell straight v apostrophe equals 2 end cell end table end style 

Berdasarkan turunan pada pembagian dua fungsi maka:

begin mathsize 14px style 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 straight u apostrophe times straight v minus straight u times straight v apostrophe over denominator straight v squared end fraction end cell row blank equals cell fraction numerator 20 open parentheses 2 x minus 1 close parentheses minus open parentheses 20 x minus 2 close parentheses 2 over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 40 x minus 20 minus 40 x plus 4 over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 16 over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell end table end style 

Dengan demikian turunan pertama dari fungsi tersebut adalah begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator negative 16 over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end style.

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