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Jika begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 2 x squared minus x minus 1 end root end style, maka carilah turunannya

Pembahasan Soal:

Misalkan begin mathsize 14px style 2 x squared minus x minus 1 equals u end style, maka begin mathsize 14px style f left parenthesis x right parenthesis equals u to the power of begin inline style 1 half end style end exponent end style.

Turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 1 half u to the power of begin inline style 1 half end style minus 1 end exponent times u apostrophe end style.

begin mathsize 14px style u equals 2 x squared minus x minus 1 u apostrophe equals 4 x minus 1 end style

Sehingga turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 2 x squared minus x minus 1 end root end style adalah sebagai berikut:

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 1 half u to the power of begin inline style 1 half end style minus 1 end exponent times u apostrophe end cell row blank equals cell 1 half u to the power of begin inline style negative 1 half end style end exponent times u apostrophe end cell row blank equals cell 1 half times fraction numerator 1 over denominator square root of u end fraction times u apostrophe end cell row blank equals cell 1 half times fraction numerator 1 over denominator square root of 2 x squared minus x minus 1 end root end fraction times 4 x minus 1 end cell row blank equals cell fraction numerator 4 x minus 1 over denominator 2 square root of 2 x squared minus x minus 1 end root end fraction end cell end table end style

Jadi, turunan fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals square root of 2 x squared minus x minus 1 end root end style adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator 2 square root of 2 x squared minus x minus 1 end root end fraction end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Dwi

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 31 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui fungsi . Turunan fungsi  adalah

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals 6 x squared plus 7 x minus 5 end style. Turunan fungsi begin mathsize 14px style f open parentheses x close parentheses end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 6 x squared plus 7 x minus 5 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 2 times 6 x plus 7 end cell row blank equals cell 12 x plus 7 end cell end table end style 

Jadi, jawaban yang tepat adalah A.

Roboguru

Jika fungsi , maka

Pembahasan Soal:

Turunan pertama dari fungsi aljabar f open parentheses x close parentheses equals a x to the power of n dapat ditentukan dengan rumus berikut.

f apostrophe open parentheses x close parentheses equals a times n x to the power of n minus 1 end exponent 

Sehingga untuk fungsi f open parentheses x close parentheses equals 2 x squared plus 6 x plus 1 dapat ditentukan turunan pertamanya sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell 2 times 2 x to the power of 2 minus 1 end exponent plus 6 times 1 x to the power of 1 minus 1 end exponent plus 1 times 0 x to the power of 0 minus 1 end exponent end cell row blank equals cell 4 x to the power of 1 plus 6 x to the power of 0 plus 0 end cell row blank equals cell 4 x plus 6 times 1 end cell row blank equals cell 4 x plus 6 end cell end table 

Dengan demikian, diperoleh 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table.

Roboguru

Turunan dari  adalah ...

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell a x to the power of n plus c end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell n times 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 cell f apostrophe open parentheses x close parentheses end cell equals cell turunan space pertama space fungsi space f left parenthesis x right parenthesis end cell row a equals cell koefisien space variabel space x end cell row n equals cell bilangan space pangkat end cell row c equals konstanta end table  

Diketahui f open parentheses x close parentheses equals x to the power of 6 minus x to the power of 5 minus 4, maka turunan fungsi tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x to the power of 6 minus x to the power of 5 minus 4 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 6 x to the power of 6 minus 1 end exponent minus 5 x to the power of 5 minus 1 end exponent minus 0 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 6 x to the power of 5 minus 5 x to the power of 4 end cell end table 

Jadi, turunan dari f open parentheses x close parentheses equals x to the power of 6 minus x to the power of 5 minus 4 adalah Error converting from MathML to accessible text..

Roboguru

Turunan pertama dari fungsi  adalah .

Pembahasan Soal:

Ingat!

begin mathsize 14px style y equals a x to the power of n comma space maka space y apostrophe equals n times a x to the power of n minus 1 end exponent y equals u times v comma space maka space y apostrophe equals u apostrophe times v plus u times v apostrophe y equals open parentheses g open parentheses x close parentheses close parentheses to the power of n comma space maka space y apostrophe equals n open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis end style     

Dengan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fungsi space awal end cell row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell row u equals cell fungsi space pertama space pada space y end cell row cell u apostrophe end cell equals cell turunan space pertama space fungsi space u space end cell row v equals cell fungsi space kedua space pada space y end cell row cell v apostrophe end cell equals cell turunan space pertama space fungs i space v end cell row a equals cell koefisien space variabel space x end cell row cell g left parenthesis x right parenthesis end cell equals cell fungsi space berpangkat end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell space turunan space pertama space dari space g apostrophe left parenthesis x right parenthesis end cell end table end style   

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x squared open parentheses 2 x minus 6 close parentheses to the power of 6 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 3 x squared end cell row cell u apostrophe end cell equals cell 2 times 3 x to the power of 2 minus 1 end exponent end cell row cell u apostrophe end cell equals cell 6 x end cell end table end style  

dan begin mathsize 14px style v equals open parentheses 2 x minus 6 close parentheses to the power of 6 end style

Karena fungsi size 14px v merupakan fungsi yang berpangkat, maka misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 6 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 1 times 2 x to the power of 1 minus 1 end exponent minus 0 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals 2 end table end style 

Sehingga, turunan fungsi size 14px v:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row v equals cell open parentheses 2 x minus 6 close parentheses to the power of 6 end cell row cell v apostrophe end cell equals cell n open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis end cell row cell v apostrophe end cell equals cell 6 open parentheses 2 x minus 6 close parentheses to the power of 6 minus 1 end exponent times 2 end cell row cell v apostrophe end cell equals cell 12 open parentheses 2 x minus 6 close parentheses to the power of 5 end cell end table end style 

Maka, turunan fungsi tersebut:

begin mathsize 14px style y apostrophe equals u apostrophe times v plus u times v apostrophe y apostrophe equals 6 x open parentheses 2 x minus 6 close parentheses to the power of 6 plus 3 x squared times 12 open parentheses 2 x minus 6 close parentheses to the power of 5 y apostrophe equals 6 x open parentheses 2 x minus 6 close parentheses to the power of 6 plus 36 x squared open parentheses 2 x minus 6 close parentheses to the power of 5 y apostrophe equals open parentheses 6 x close parentheses open parentheses 2 x minus 6 close parentheses open parentheses 2 x minus 6 close parentheses to the power of 5 plus 36 x squared open parentheses 2 x minus 6 close parentheses to the power of 5 y apostrophe equals open parentheses 12 x squared minus 36 x close parentheses open parentheses 2 x minus 6 close parentheses to the power of 5 plus 36 x squared open parentheses 2 x minus 6 close parentheses to the power of 5 y apostrophe equals open parentheses 12 x squared plus 36 x squared minus 36 x close parentheses open parentheses 2 x minus 6 close parentheses to the power of 5 y apostrophe equals open parentheses 48 x squared minus 36 x close parentheses open parentheses 2 x minus 6 close parentheses to the power of 5 y apostrophe equals 12 x open parentheses 4 x minus 3 close parentheses open parentheses 2 x minus 6 close parentheses to the power of 5 end style  

Sehingga, turunan fungsi tersebut adalah begin mathsize 14px style y apostrophe equals 12 x open parentheses 4 x minus 3 close parentheses open parentheses 2 x minus 6 close parentheses to the power of 5 end style.

Jadi, tidak ada jawaban yang tepat.

Roboguru

Turunan pertama dari fungsi  adalah

Pembahasan Soal:

Perhatikan perhitungan berikut.

Ingat, aturan rantai pada turunan:

begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator d f open parentheses u close parentheses over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end style

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 10 open parentheses 5 x squared minus 3 close parentheses to the power of 4 end style, maka:

Misal:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 5 x squared minus 3 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 2 times 5 x to the power of 2 minus 1 end exponent end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 10 x end cell end table end style

kemudian

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses u close parentheses end cell equals cell 10 u to the power of 4 end cell row cell fraction numerator d f open parentheses u close parentheses over denominator d u end fraction end cell equals cell 4 times 10 u to the power of 4 minus 1 end exponent end cell row cell fraction numerator d f open parentheses u close parentheses over denominator d u end fraction end cell equals cell 40 u cubed end cell end table end style


Sehingga:

begin mathsize 14px style 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 d f left parenthesis u right parenthesis over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row blank equals cell 40 u cubed times 10 x end cell row blank equals cell 400 x u cubed end cell row blank equals cell 400 x open parentheses 5 x squared minus 3 close parentheses cubed end cell end table end style

Jadi, turunan pertama dari fungsi begin mathsize 14px style f open parentheses x close parentheses equals 10 open parentheses 5 x squared minus 3 close parentheses to the power of 4 end style adalah begin mathsize 14px style 400 table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 5 x squared minus 3 close parentheses end cell end table cubed end style.

Dengan demikian, jawaban yang tepat adalah E.

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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