Pertanyaan

Turunan kedua fungsi h ( x ) = 3 x 2 x − 1 adalah....

Turunan kedua fungsi $h (x) = \frac{2 x - 1}{3 x}$ adalah....

$begin mathsize 14px style h to the power of apostrophe apostrophe end exponent left parenthesis x right parenthesis equals negative fraction numerator 2 over denominator 3 x to the power of 4 end fraction end style$
$size 14px h to the power of size 14px apostrophe size 14px apostrophe end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px minus fraction numerator size 14px 2 over denominator size 14px 3 size 14px x to the power of size 14px 3 end fraction$
$size 14px h to the power of size 14px apostrophe size 14px apostrophe end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px 1 over denominator size 14px 3 size 14px x to the power of size 14px 2 end fraction$
$size 14px h to the power of size 14px apostrophe size 14px apostrophe end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px 2 over denominator size 14px 3 size 14px x to the power of size 14px 3 end fraction$
$size 14px h to the power of size 14px apostrophe size 14px apostrophe end exponent size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals fraction numerator size 14px 2 over denominator size 14px 3 size 14px x to the power of size 14px 4 end fraction$

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Konsep turunan yang digunakan untuk menyelesaikan soal di atas adalah untuk setiap . Diketahui . Turunan pertama fungsi ditulis , sementara turunan kedua fungsi ditulis , sehingga Jadi, jawaban yang benar adalah B.

Konsep turunan yang digunakan untuk menyelesaikan soal di atas adalah

$begin mathsize 14px style fraction numerator d blank over denominator d x end fraction straight a x to the power of n equals straight a times n x to the power of n minus 1 end exponent end style$

untuk setiap .
Diketahui $begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator 3 x end fraction equals 2 over 3 minus fraction numerator 1 over denominator 3 x end fraction end style$ . Turunan pertama fungsi ditulis , sementara turunan kedua fungsi ditulis , sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h apostrophe apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator d blank over denominator d x end fraction h apostrophe left parenthesis x right parenthesis end cell row blank equals cell fraction numerator d blank over denominator d x end fraction open parentheses fraction numerator d blank over denominator d x end fraction h left parenthesis x right parenthesis close parentheses end cell row blank equals cell fraction numerator d blank over denominator d x end fraction open parentheses fraction numerator d blank over denominator d x end fraction open parentheses 2 over 3 minus fraction numerator 1 over denominator 3 x end fraction close parentheses close parentheses end cell row blank equals cell fraction numerator d blank over denominator d x end fraction open parentheses negative 1 third times negative 1 x to the power of negative 1 minus 1 end exponent close parentheses end cell row blank equals cell fraction numerator d blank over denominator d x end fraction open parentheses 1 third times x to the power of negative 2 end exponent close parentheses end cell row blank equals cell 1 third times left parenthesis negative 2 right parenthesis x to the power of negative 2 minus 1 end exponent end cell row blank equals cell negative fraction numerator 2 over denominator 3 x cubed end fraction end cell end table end style$

Jadi, jawaban yang benar adalah B.