Roboguru

Dengan menggunakan konsep turunan, tentukan turuna...

Dengan menggunakan konsep turunan, tentukan turunan dari fungsi berikut.

c. begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed open parentheses 2 x plus 1 close parentheses to the power of 5 end style  

Jawaban:

Ingat!

Aturan Rantai:

begin mathsize 14px style y equals left parenthesis g left parenthesis x right parenthesis right parenthesis to the power of n comma space maka space y apostrophe equals n times left parenthesis g left parenthesis x right parenthesis right parenthesis to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis y equals u times v comma space maka space y apostrophe equals u apostrophe times v plus u times v apostrophe end style   

Dengan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fungsi space awal end cell row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell row cell g left parenthesis x right parenthesis end cell equals cell fungsi space yang space dipangkatkan end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell turunan space pertama space fungsi space g left parenthesis x right parenthesis end cell row u equals cell fungsi space pertama space pada space y end cell row v equals cell fungsi space kedua space pada space y end cell row cell u apostrophe end cell equals cell turunan space pertama space fungsi space u end cell row cell v apostrophe end cell equals cell turunan space pertama space fungsi space v end cell end table end style  

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed open parentheses 2 x plus 1 close parentheses to the power of 5 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x cubed end cell row cell u apostrophe end cell equals cell 3 x to the power of 3 minus 1 end exponent end cell row cell u apostrophe end cell equals cell 3 x squared end cell end table end style 

dan begin mathsize 14px style v equals open parentheses 2 x plus 1 close parentheses to the power of 5 end style

Karena fungsi size 14px v merupakan fungsi yang berpangkat, maka misalkan:

undefined

Sehingga, turunan fungsi size 14px v:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row v equals cell open parentheses 2 x plus 1 close parentheses to the power of 5 end cell row cell v apostrophe end cell equals cell n open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis end cell row cell v apostrophe end cell equals cell 5 open parentheses 2 x plus 1 close parentheses to the power of 5 minus 1 end exponent times 2 end cell row cell v apostrophe end cell equals cell 10 open parentheses 2 x plus 1 close parentheses to the power of 4 end cell end table end style 

Maka, turunan fungsi tersebut:

      begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x cubed open parentheses 2 x plus 1 close parentheses to the power of 5 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell u apostrophe times v plus u times v apostrophe end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 3 x squared open parentheses 2 x plus 1 close parentheses to the power of 5 plus x cubed times 10 open parentheses 2 x plus 1 close parentheses to the power of 4 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 3 x squared open parentheses 2 x plus 1 close parentheses to the power of 5 plus 10 x cubed open parentheses 2 x plus 1 close parentheses to the power of 4 end cell end table end style 

Jadi, turunan fungsi tersebut adalah Error converting from MathML to accessible text..

0

Ruangguru

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