Iklan

Iklan

Pertanyaan

Turunan pertama dari fungsi f ( x ) = 3 x − x 2 ​ adalah ...

Turunan pertama dari fungsi  adalah ...space 

Iklan

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

turunan pertama fungsi adalah .

 turunan pertama fungsi f open parentheses x close parentheses equals cube root of x minus x squared end root adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus 2 x over denominator 3 cube root of open parentheses x minus x squared close parentheses squared end root end fraction end cell end table.

Iklan

Pembahasan

Ingat! dengan: Misalkan ,maka: Turunan pertama fungsi . Jadi,turunan pertama fungsi adalah .

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell a x to the power of n end cell row cell y apostrophe end cell equals cell n times a x to the power of n minus 1 end exponent end cell row cell f open parentheses x close parentheses end cell equals cell u to the power of n end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell n times u to the power of n minus 1 end exponent times u apostrophe end cell end table 

dengan:

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell koefisien space dari space x end cell row n equals pangkat row u equals cell fungsi space pada space f left parenthesis x right parenthesis end cell row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell turunan space pertama space fungsi space f left parenthesis x right parenthesis end cell row cell u apostrophe end cell equals cell turunan space pertama space fungsi space u end cell end table 

Misalkan u equals x minus x squared, maka:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x minus x squared end cell row cell u apostrophe end cell equals cell x to the power of 1 minus 1 end exponent minus 2 x to the power of 2 minus 1 end exponent end cell row cell u apostrophe end cell equals cell 1 minus 2 x end cell end table  

Turunan pertama fungsi f open parentheses x close parentheses equals cube root of x minus x squared end root

 table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell cube root of u end cell row cell f open parentheses x close parentheses end cell equals cell u to the power of 1 third end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 1 third u to the power of 1 third minus 1 end exponent times u apostrophe end cell row blank equals cell 1 third u to the power of negative 2 over 3 end exponent times u apostrophe end cell row blank equals cell fraction numerator u apostrophe over denominator 3 u to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator u apostrophe over denominator 3 cube root of u squared end root end fraction end cell row blank equals cell fraction numerator 1 minus 2 x over denominator 3 cube root of open parentheses x minus x squared close parentheses squared end root end fraction end cell end table 

Jadi, turunan pertama fungsi f open parentheses x close parentheses equals cube root of x minus x squared end root adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus 2 x over denominator 3 cube root of open parentheses x minus x squared close parentheses squared end root end fraction end cell end table.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

27

Zhara Delvia Putri

Pembahasan lengkap banget

Iklan

Iklan

Pertanyaan serupa

Diketahui f ( x ) = ( 3 x 3 − 2 x 2 + x − 1 ) 3 . Turunan pertama fungsi f adalah ...

8

4.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia