Roboguru

Jika  merupakan turunan  maka nilai ...

Pertanyaan

Jika begin mathsize 14px style f apostrophe open parentheses x close parentheses end style merupakan turunan begin mathsize 14px style f open parentheses x close parentheses equals square root of 6 x plus 7 end root end style maka nilai begin mathsize 14px style f apostrophe open parentheses 3 close parentheses equals end style...

  1. begin mathsize 14px style 2 over 3 end style 

  2. begin mathsize 14px style 3 over 5 end style 

  3. begin mathsize 14px style 5 over 7 end style 

  4. begin mathsize 14px style 7 over 9 end style 

  5. begin mathsize 14px style 9 over 13 end style 

Pembahasan Soal:

Jika begin mathsize 14px style f apostrophe open parentheses x close parentheses end style merupakan turunan begin mathsize 14px style f open parentheses x close parentheses equals square root of 6 x plus 7 end root end style , misalkan begin mathsize 14px style u equals 6 x plus 7 end style maka begin mathsize 14px style u apostrophe equals 6 end style. Gunakan konsep aturan rantai maka diperoleh begin mathsize 14px style f apostrophe open parentheses x close parentheses end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell square root of 6 x plus 7 end root end cell row cell f open parentheses x close parentheses end cell equals cell square root of u end cell row cell f open parentheses x close parentheses end cell equals cell u to the power of 1 half end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 1 half u to the power of 1 half minus 1 end exponent times u apostrophe end cell row blank equals cell 1 half u to the power of negative 1 half end exponent times 6 end cell row blank equals cell 3 u to the power of negative 1 half end exponent end cell row blank equals cell 3 over u to the power of begin display style 1 half end style end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 3 over denominator square root of 6 x plus 7 end root end fraction end cell end table end style 

Kemudian substitusikan nilai begin mathsize 14px style x equals 3 end style sehingga:

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 3 over denominator square root of 6 x plus 7 end root end fraction end cell row cell f apostrophe open parentheses 3 close parentheses end cell equals cell fraction numerator 3 over denominator square root of 6 open parentheses 3 close parentheses plus 7 end root end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 18 plus 7 end root end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 25 end fraction end cell row blank equals cell 3 over 5 end cell end table end style 

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved