Diketahui fungsi f(x)=x2−3x+2(x+2)2​. Tentukan turunan pertama fungsi f(x).

Pertanyaan

Diketahui fungsi f open parentheses x close parentheses equals fraction numerator open parentheses x plus 2 close parentheses squared over denominator x squared minus 3 x plus 2 end fraction. Tentukan turunan pertama fungsi f open parentheses x close parentheses.space 

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

 turunan pertama fungsi f open parentheses x close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 7 x squared minus 4 x plus 20 over denominator open parentheses x squared minus 3 x plus 2 close parentheses squared end fraction end cell end table.

Pembahasan

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell u over v end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row y equals cell a x to the power of n plus c end cell row cell y apostrophe end cell equals cell n a x to the power of n minus 1 end exponent end cell end table  

Keterangan:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell fungsi space pada space pembilang end cell row v equals cell fungsi space pada space penyebut end cell row cell u apostrophe end cell equals cell turunan space pertama space fungs i space u end cell row cell v apostrophe end cell equals cell turunan space pertama space fungsi space v end cell row a equals cell koefisien space variabel space x end cell row n equals cell bilangan space berpangkat end cell row c equals kostanta row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell end table  

Diketahui f open parentheses x close parentheses equals fraction numerator open parentheses x plus 2 close parentheses squared over denominator x squared minus 3 x plus 2 end fraction, maka:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell open parentheses x plus 2 close parentheses squared end cell row u equals cell x squared plus 4 x plus 4 end cell row cell u apostrophe end cell equals cell 2 x to the power of 2 minus 1 end exponent plus 4 x to the power of 1 minus 1 end exponent plus 0 end cell row cell u apostrophe end cell equals cell 2 x plus 4 end cell row v equals cell x squared minus 3 x plus 2 end cell row cell v apostrophe end cell equals cell 2 x to the power of 2 minus 1 end exponent minus 3 x to the power of 1 minus 1 end exponent plus 0 end cell row cell v apostrophe end cell equals cell 2 x minus 3 end cell end table 

Sehingga, turunan pertama fungsi f open parentheses x close parentheses:

 table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses 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 open parentheses x close parentheses end cell equals cell fraction numerator open parentheses 2 x plus 4 close parentheses open parentheses x squared minus 3 x plus 2 close parentheses minus open parentheses x squared plus 4 x plus 4 close parentheses open parentheses 2 x minus 3 close parentheses over denominator open parentheses x squared minus 3 x plus 2 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 x cubed minus 2 x squared minus 8 x plus 8 minus open parentheses 2 x cubed plus 5 x squared minus 4 x minus 12 close parentheses over denominator open parentheses x squared minus 3 x plus 2 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 x cubed minus 2 x squared minus 8 x plus 8 minus 2 x cubed minus 5 x squared plus 4 x plus 12 over denominator open parentheses x squared minus 3 x plus 2 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator negative 7 x squared minus 4 x plus 20 over denominator open parentheses x squared minus 3 x plus 2 close parentheses squared end fraction end cell end table 

Jadi, turunan pertama fungsi f open parentheses x close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 7 x squared minus 4 x plus 20 over denominator open parentheses x squared minus 3 x plus 2 close parentheses squared end fraction end cell end table.

64

4.5 (2 rating)

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