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Turunan pertama dari  adalah ..

Pertanyaan

Turunan pertama dari y equals fraction numerator 3 x minus 4 over denominator x plus 2 end fraction adalah ..

Pembahasan Soal:

Turunan pertama dari y equals fraction numerator 3 x minus 4 over denominator x plus 2 end fraction adalah ..

y equals fraction numerator 3 x minus 4 over denominator x plus 2 end fraction

Misal :

table attributes columnalign right center left columnspacing 0px end attributes row cell u space end cell equals cell 3 x minus 4 rightwards arrow d u space equals 3 end cell row cell v space end cell equals cell x space plus 2 space rightwards arrow d v equals 1 end cell end table

jadi hasil turunannya

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 3 x minus 4 over denominator x plus 2 end fraction equals u over v end cell row cell y apostrophe 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 3 open parentheses x plus 2 close parentheses minus 1 open parentheses 3 x minus 4 close parentheses over denominator open parentheses x plus 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 3 x plus 6 minus 3 x plus 4 over denominator x squared plus 4 x plus 4 end fraction end cell row blank equals cell fraction numerator 10 over denominator x squared plus 4 x plus 4 end fraction end cell end table

Jadi, Turunan pertama dari y equals fraction numerator 3 x minus 4 over denominator x plus 2 end fraction adalah fraction numerator 10 over denominator x squared plus 4 x plus 4 end fraction.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Rahmawati

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 06 Juni 2021

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Diketahui . Turunan pertama fungsi g adalah...

Pembahasan Soal:

Ingat rumus turunan aljabar begin mathsize 14px style y equals a x to the power of n rightwards arrow y apostrophe equals a n x to the power of n minus 1 end exponent end style  dan sifat turunan pada pembagian fungsi begin mathsize 14px style y equals u over v rightwards arrow y apostrophe equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight g left parenthesis straight x right parenthesis end cell equals cell fraction numerator 5 straight x minus 1 over denominator 3 straight x plus 4 end fraction end cell row cell straight g apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 5 left parenthesis 3 straight x plus 4 right parenthesis minus left parenthesis 5 straight x minus 1 right parenthesis 3 over denominator left parenthesis 3 straight x plus 4 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 15 straight x plus 20 minus 15 straight x plus 3 over denominator left parenthesis 3 straight x plus 4 right parenthesis squared end fraction end cell row blank equals cell 23 over left parenthesis 3 straight x plus 4 right parenthesis squared end cell end table end style

Jadi, diperoleh hasil turunannya adalah begin mathsize 14px style straight g apostrophe left parenthesis straight x right parenthesis equals 23 over left parenthesis 3 straight x plus 4 right parenthesis squared end style.

2

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. Tentukan .

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

dengan:

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 fungsi space u end cell row cell v apostrophe end cell equals cell turunan space pertama space fungsi space v end cell end table 

Maka,

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

Sehingga, turunan pertama fungsi tersebut:

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 v apostrophe times u over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 x minus 3 close parentheses open parentheses x squared plus 2 x plus 1 close parentheses minus open parentheses 2 x plus 2 close parentheses open parentheses x squared minus 3 x close parentheses over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 x cubed plus x squared minus 4 x minus 3 close parentheses minus open parentheses 2 x cubed minus 4 x squared minus 6 x close parentheses over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x cubed plus x squared minus 4 x minus 3 minus 2 x cubed plus 4 x squared plus 6 x over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 5 x squared minus 2 x minus 3 over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell end table 

Maka, nilai f apostrophe open parentheses 2 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 5 x squared minus 2 x minus 3 over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell row cell f apostrophe open parentheses 2 close parentheses end cell equals cell fraction numerator 5 times 2 squared minus 2 times 2 minus 3 over denominator open parentheses 2 squared plus 2 times 2 plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 20 minus 4 minus 3 over denominator 9 squared end fraction end cell row blank equals cell 13 over 81 end cell end table 

Jadi, nilai f apostrophe open parentheses 2 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 13 over 81 end cell end table.

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Dengan menggunakan teorema-teorema turunan fungsi, tentukan turunan pertama dari fungsi bawah ini.

Pembahasan Soal:

Ingat:

1. y 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 cell a x to the power of n space end cell rightwards arrow cell y apostrophe equals a times n times x to the power of n minus 1 end exponent end cell end table 

2. y equals u over v rightwards arrow y apostrophe equals fraction numerator u apostrophe times v plus u times v apostrophe over denominator v squared end fraction 

Maka turunan y equals fraction numerator 2 x squared minus 3 x plus 1 over denominator 2 x plus 1 end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 times 2 x squared minus 3 close parentheses open parentheses 2 x plus 1 close parentheses minus open parentheses 2 x squared minus 3 x plus 1 close parentheses open parentheses 2 close parentheses over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 4 x minus 3 close parentheses open parentheses 2 x plus 1 close parentheses minus open parentheses 4 x squared minus 6 x plus 2 close parentheses over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 8 x squared plus 4 x minus 6 x minus 3 minus 4 x squared plus 6 x minus 2 over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 4 x squared plus 4 x minus 5 over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell end table 

Jadi turunan fungsi dari undefined adalah begin mathsize 14px style y to the power of apostrophe equals fraction numerator 4 x squared plus 4 x minus 5 over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end style.

0

Roboguru

Tentukan  dan  untuk , , dan  konstanta. c.

Pembahasan Soal:

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d. Jika  dan , tentukan .

Pembahasan Soal:

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