Roboguru

Dengan menggunakan konsep turunan, tentukan turuna...

Dengan menggunakan konsep turunan, tentukan turunan dari fungsi berikut.

e. begin mathsize 14px style f left parenthesis x right parenthesis equals open parentheses 1 half x squared minus 1 third x close parentheses to the power of 4 end style

Jawaban:

Ingat!

Aturan Rantai:

begin mathsize 14px style y equals open parentheses g open parentheses x close parentheses close parentheses to the power of n comma space maka space y apostrophe equals n times 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 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 open parentheses x close parentheses end cell equals cell fungsi space yang space dipangkatkan end cell row cell g apostrophe open parentheses x close parentheses end cell equals cell turunan space pertama space fungsi space g left parenthesis x right parenthesis end cell end table end style 

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals open parentheses 1 half x squared minus 1 third x close parentheses to the power of 4 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 1 half x squared minus 1 third x end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 1 half times 2 x to the power of 2 minus 1 end exponent minus 1 third x to the power of 1 minus 1 end exponent end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell x minus 1 third end cell end table end style   

Sehingga 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 open parentheses 1 half x squared minus 1 third x close parentheses to the power of 4 end cell row cell f apostrophe left parenthesis x right parenthesis 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 f apostrophe left parenthesis x right parenthesis end cell equals cell 4 open parentheses 1 half x squared minus 1 third x close parentheses to the power of 4 minus 1 end exponent times open parentheses x minus 1 third close parentheses end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 4 open parentheses x minus 1 third close parentheses open parentheses 1 half x squared minus 1 third x close parentheses cubed end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell open parentheses 4 x minus 4 over 3 close parentheses open parentheses 1 half x squared minus 1 third x close parentheses cubed end cell end table end style    

Jadi, turunan fungsi tersebut adalah begin mathsize 14px style open parentheses 4 x minus 4 over 3 close parentheses open parentheses 1 half x squared minus 1 third x close parentheses cubed end style.

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