Pertanyaan

Jika f ( x ) = 2 x 2 − x − 1 ​ ,maka carilah turunannya

Jika , maka carilah turunannya

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

turunan fungsi adalah .

turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 2 x squared minus x minus 1 end root end style adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator 2 square root of 2 x squared minus x minus 1 end root end fraction end style

Pembahasan

Misalkan , maka . Turunan fungsi adalah . Sehingga turunan fungsi adalah sebagai berikut: Jadi, turunan fungsi adalah .

Misalkan begin mathsize 14px style 2 x squared minus x minus 1 equals u end style, maka begin mathsize 14px style f left parenthesis x right parenthesis equals u to the power of begin inline style 1 half end style end exponent end style.

Turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 1 half u to the power of begin inline style 1 half end style minus 1 end exponent times u apostrophe end style.

begin mathsize 14px style u equals 2 x squared minus x minus 1 u apostrophe equals 4 x minus 1 end style

Sehingga turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 2 x squared minus x minus 1 end root end style adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 1 half u to the power of begin inline style 1 half end style minus 1 end exponent times u apostrophe end cell row blank equals cell 1 half u to the power of begin inline style negative 1 half end style end exponent times u apostrophe end cell row blank equals cell 1 half times fraction numerator 1 over denominator square root of u end fraction times u apostrophe end cell row blank equals cell 1 half times fraction numerator 1 over denominator square root of 2 x squared minus x minus 1 end root end fraction times 4 x minus 1 end cell row blank equals cell fraction numerator 4 x minus 1 over denominator 2 square root of 2 x squared minus x minus 1 end root end fraction end cell end table end style

Jadi, turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 2 x squared minus x minus 1 end root end style adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator 2 square root of 2 x squared minus x minus 1 end root end fraction end style

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