Pertanyaan

Tentukan turunan fungsi berikut ini: b. f ( x ) = 3 x − 4 3 x 3 + 3 x

Tentukan turunan fungsi berikut ini:

b. $f (x) = \frac{3 x ^{3} + 3 x}{3 x - 4}$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

turunan pertama fungsi adalah .

turunan pertama fungsi

adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 18 x cubed minus 36 x squared minus 14 over denominator open parentheses 3 x minus 4 close parentheses squared end fraction end cell end table end style$ .

Pembahasan

Ingat! Dengan: , maka: Sehingga, turunan pertama fungsi adalah: Jadi,turunan pertama fungsi adalah .

Ingat!

$begin mathsize 14px style f left parenthesis x right parenthesis equals u over v comma space maka space f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end style$

Dengan:

$begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 3 x cubed plus 3 x over denominator 3 x minus 4 end fraction end style$ , maka:

Sehingga, turunan pertama fungsi adalah:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator open parentheses 9 x squared plus 3 close parentheses open parentheses 3 x minus 4 close parentheses minus open parentheses 3 x cubed plus 3 x close parentheses times 3 over denominator open parentheses 3 x minus 4 close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 27 x cubed minus 36 x squared plus 9 x minus 14 minus 9 x cubed minus 9 x over denominator open parentheses 3 x minus 4 close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 18 x cubed minus 36 x squared minus 14 over denominator open parentheses 3 x minus 4 close parentheses squared end fraction end cell end table end style$

Jadi, turunan pertama fungsi adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 18 x cubed minus 36 x squared minus 14 over denominator open parentheses 3 x minus 4 close parentheses squared end fraction end cell end table end style$ .