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Pertanyaan

Tentukan turunan pertama dari fungsi:

c. f left parenthesis x right parenthesis equals fraction numerator 4 x plus 6 over denominator square root of 3 x minus 1 end root end fraction!

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

 turunan pertama dari fungsi tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x minus 13 over denominator square root of open parentheses 3 x minus 1 close parentheses cubed end root end fraction end cell end table.

Pembahasan

Ingat kembali rumus turunan pada pecahan dua fungsi sebagai berikut.

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 u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell end table

Dengan rumus di atas, maka didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 4 x plus 6 end cell row cell u apostrophe end cell equals 4 row v equals cell square root of 3 x minus 1 end root end cell row blank equals cell open parentheses 3 x minus 1 close parentheses to the power of 1 half end exponent end cell row cell v apostrophe end cell equals cell 3 over 2 open parentheses 3 x minus 1 close parentheses to the power of negative 1 half end exponent end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 3 x minus 1 end root end fraction end cell row blank blank blank row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator 4 times open parentheses 3 x minus 1 close parentheses blank to the power of begin display style 1 half end style end exponent minus begin display style fraction numerator 3 over denominator 2 square root of 3 x minus 1 end root end fraction end style times open parentheses 4 x plus 6 close parentheses over denominator open parentheses open parentheses 3 x minus 1 close parentheses blank to the power of 1 half end exponent close parentheses squared end fraction end cell row blank equals cell fraction numerator 4 square root of 3 x minus 1 end root minus begin display style fraction numerator 6 x plus 9 over denominator square root of 3 x minus 1 end root end fraction end style over denominator 3 x minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 4 open parentheses 3 x minus 1 close parentheses minus open parentheses 6 x plus 9 close parentheses over denominator square root of 3 x minus 1 end root end fraction end style over denominator 3 x minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 12 x minus 4 minus open parentheses 6 x plus 9 close parentheses over denominator square root of 3 x minus 1 end root end fraction end style over denominator 3 x minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 6 x minus 13 over denominator square root of 3 x minus 1 end root end fraction end style over denominator 3 x minus 1 end fraction end cell row blank equals cell fraction numerator 6 x minus 13 over denominator open parentheses 3 x minus 1 close parentheses square root of 3 x minus 1 end root end fraction end cell row blank equals cell fraction numerator 6 x minus 13 over denominator square root of open parentheses 3 x minus 1 close parentheses cubed end root end fraction end cell end table

Dengan demikian, turunan pertama dari fungsi tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x minus 13 over denominator square root of open parentheses 3 x minus 1 close parentheses cubed end root end fraction end cell end table.

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