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Tentukan turunan kedua fungsi berikut ! f(x)=(3x2+2x−1)2

Pertanyaan

Tentukan turunan kedua fungsi berikut !

begin mathsize 14px style f open parentheses x close parentheses equals open parentheses 3 x squared plus 2 x minus 1 close parentheses squared space space space space space space space end style  

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

 begin mathsize 14px style f open parentheses x close parentheses equals open parentheses 3 x squared plus 2 x minus 1 close parentheses squared space space space space space space space end style 
Turunan pertama dari fungsi tersebut  

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style end cell size 14px equals cell begin mathsize 14px style left parenthesis 3 x squared plus 2 x minus 1 right parenthesis end style to the power of size 14px 2 end cell row cell size 14px f size 14px apostrophe begin mathsize 14px style left parenthesis x right parenthesis end style end cell size 14px equals cell size 14px 2 begin mathsize 14px style left parenthesis 3 x squared plus 2 x minus 1 right parenthesis end style begin mathsize 14px style left parenthesis 6 x plus 2 right parenthesis end style end cell row cell size 14px f size 14px apostrophe begin mathsize 14px style left parenthesis x right parenthesis end style end cell size 14px equals cell begin mathsize 14px style left parenthesis 12 x plus 4 right parenthesis end style size 14px left parenthesis size 14px 3 size 14px x to the power of size 14px 2 size 14px plus size 14px 2 size 14px x size 14px minus size 14px 1 size 14px right parenthesis end cell row blank blank blank row blank blank cell size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space end cell end table 

Selanjutnya akan ditentukan turunan kedua

begin mathsize 14px style u equals left parenthesis 12 x plus 4 right parenthesis space space space space space space space space v equals left parenthesis 3 x squared plus 2 x minus 1 right parenthesis u apostrophe equals 12 space space space space space space space space space space space space space space space space v apostrophe equals 6 x plus 2 f double apostrophe left parenthesis x right parenthesis equals u apostrophe v plus v apostrophe u space space space space space space space space space equals 12 left parenthesis 3 x squared plus 2 x minus 1 right parenthesis plus left parenthesis 6 x plus 2 right parenthesis left parenthesis 12 x plus 4 right parenthesis space space space space space space space space space equals 36 x squared plus 24 x minus 12 plus 72 x squared plus 48 x plus 8 space space space space space space space space space equals 108 x squared plus 72 x minus 4 end style 

 Jadi, turunan kedua fungsi tersebut adalah begin mathsize 14px style f double apostrophe open parentheses x close parentheses equals 108 x squared plus 72 x minus 4 end style

 

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