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Turunan pertama dari  adalah ...

Pertanyaan

Turunan pertama dari f open parentheses x close parentheses equals open parentheses 5 x plus 3 close parentheses cubed adalah ... 

  1. open parentheses 15 x plus 9 close parentheses squared 

  2. 3 open parentheses 5 x plus 3 close parentheses squared 

  3. 5 open parentheses 5 x plus 3 close parentheses squared 

  4. 3 open parentheses 5 x plus 3 close parentheses squared 

  5. 15 open parentheses 5 x plus 3 close parentheses squared 

Pembahasan Soal:

Diketahui f open parentheses x close parentheses equals open parentheses 5 x plus 3 close parentheses cubed

Dengan mengunakan konsep turunan aturan rantai, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell open parentheses 3 close parentheses times open parentheses 5 x plus 3 close parentheses squared times open parentheses 5 close parentheses end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 15 open parentheses 5 x plus 3 close parentheses squared end cell end table 

Jadi, turunan pertama dari f open parentheses x close parentheses equals open parentheses 5 x plus 3 close parentheses cubed adalah f apostrophe open parentheses x close parentheses equals 15 open parentheses 5 x plus 3 close parentheses squared

Dengan demikian, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Rante

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 07 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Carilah turunan fungsi aljabar berikut ini:

Pembahasan Soal:

Ingat!

Aturan Rantai:

begin mathsize 14px style 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 times 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 cell g open parentheses x close parentheses end cell equals cell fungsi space yang space dipangkatkan end cell row cell g apostrophe open parentheses x close parentheses end cell equals cell turunan space pertama space fungsi space g left parenthesis x right parenthesis end cell end table end style 

Diketahui begin mathsize 14px style y equals f left parenthesis x right parenthesis equals open parentheses x squared minus 2 x plus 1 close parentheses squared end style, maka:

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 x squared minus 2 x plus 1 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 2 times x to the power of 2 minus 1 end exponent minus 2 x to the power of 1 minus 1 end exponent plus 0 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 2 x minus 2 end cell end table end style 

Sehingga turunan pertama fungsi begin mathsize 14px style y end style adalah:

begin mathsize 14px style y apostrophe equals n times open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe open parentheses x close parentheses y apostrophe equals 2 times open parentheses x squared minus 2 x plus 1 close parentheses to the power of 2 minus 1 end exponent times open parentheses 2 x minus 2 close parentheses y apostrophe equals 2 open parentheses 2 x minus 2 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses y apostrophe equals open parentheses 4 x minus 4 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses end style  

Jadi, turunan pertama fungsi begin mathsize 14px style y end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 4 x minus 4 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x squared minus 2 x plus 1 right parenthesis end cell end table end style.

0

Roboguru

Diberikan fungsi . Turunan pertama dari  adalah ....

Pembahasan Soal:

Ingat!

Menentukan nilai f apostrophe left parenthesis x right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell u to the power of n end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell n times u to the power of n minus 1 end exponent times u apostrophe end cell end table

Diketahui:

h open parentheses x close parentheses equals open parentheses x squared plus 3 x minus 1 close parentheses to the power of 5 

Misalkan 

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared plus 3 x minus 1 end cell row cell u apostrophe end cell equals cell 2 x plus 3 end cell end table

Sehingga dapat ditentukan turunan pertama h open parentheses x close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell u to the power of 5 end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell 5 times u to the power of 5 minus 1 end exponent times u apostrophe end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell 5 times left parenthesis x squared plus 3 x minus 1 right parenthesis to the power of 4 times left parenthesis 2 x plus 3 right parenthesis end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell left parenthesis 10 x plus 15 right parenthesis left parenthesis x squared plus 3 x minus 1 right parenthesis to the power of 4 end cell end table

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Turunan dari  adalah

Pembahasan Soal:

Turunan dari begin mathsize 14px style y equals open parentheses 3 x minus 2 close parentheses cubed open parentheses 2 x plus 1 close parentheses squared end style adalah begin mathsize 14px style horizontal ellipsis end style 

Misalkan begin mathsize 14px style u equals open parentheses 3 x minus 2 close parentheses cubed end style, maka 

begin mathsize 14px style u apostrophe equals 3 open parentheses 3 x minus 2 close parentheses squared times open parentheses 3 close parentheses equals 9 open parentheses 3 x minus 2 close parentheses squared end style.

Dan misalkan begin mathsize 14px style v equals open parentheses 2 x plus 1 close parentheses squared end style, maka 

size 14px v size 14px apostrophe size 14px equals size 14px 2 begin mathsize 14px style left parenthesis 2 x plus 1 right parenthesis end style begin mathsize 14px style left parenthesis 2 right parenthesis end style size 14px equals size 14px 4 begin mathsize 14px style left parenthesis 2 x plus 1 right parenthesis end style.

Karena begin mathsize 14px style y equals u v end style, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell u apostrophe v plus u v apostrophe end cell row blank equals cell open parentheses 9 open parentheses 3 x minus 2 close parentheses squared close parentheses open parentheses 2 x plus 1 close parentheses squared plus open parentheses 3 x minus 2 close parentheses cubed open parentheses 4 open parentheses 2 x plus 1 close parentheses close parentheses end cell row blank equals cell 9 open parentheses 3 x minus 2 close parentheses squared open parentheses 2 x plus 1 close parentheses squared plus 4 open parentheses 3 x minus 2 close parentheses cubed open parentheses 2 x plus 1 close parentheses end cell end table

Jadi, jawaban yang tepat adalah B.

0

Roboguru

1. Tentukan turunan pertama  dari fungsi berikut! a.

Pembahasan Soal:

Perhatikan penghitungan berikut!

 begin mathsize 14px style y equals 1 over open parentheses 3 x squared plus x minus 1 close parentheses squared y equals open parentheses 3 x squared plus x minus 1 close parentheses to the power of negative 2 end exponent fraction numerator d y over denominator d x end fraction equals negative 2 open parentheses 3 x squared plus x minus 1 close parentheses to the power of negative 2 minus 1 space end exponent open parentheses 2 times 3 x plus 1 minus 0 close parentheses fraction numerator d y over denominator d x end fraction equals negative 2 open parentheses 3 x squared plus x minus 1 close parentheses to the power of negative 3 space end exponent open parentheses 6 x plus 1 close parentheses fraction numerator d y over denominator d x end fraction equals fraction numerator negative 2 open parentheses 6 x plus 1 close parentheses over denominator open parentheses 3 x squared plus x minus 1 close parentheses to the power of 3 space end exponent end fraction fraction numerator d y over denominator d x end fraction equals fraction numerator negative 12 x minus 2 over denominator open parentheses 3 x squared plus x minus 1 close parentheses to the power of 3 space end exponent end fraction space end style    

Jadi, turunan pertama dari fungsi tersebut adalah begin mathsize 14px style fraction numerator d y over denominator d x end fraction equals fraction numerator negative 12 x minus 2 over denominator open parentheses 3 x squared plus x minus 1 close parentheses to the power of 3 space end exponent end fraction space end style .   

0

Roboguru

Turunan pertama dari fungsi  adalah ...

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell a x to the power of n end cell row cell y apostrophe end cell equals cell n times a x to the power of n minus 1 end exponent end cell row cell f open parentheses x close parentheses end cell equals cell u to the power of n end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell n times u to the power of n minus 1 end exponent times u apostrophe end cell end table 

dengan:

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell koefisien space dari space x end cell row n equals pangkat row u equals cell fungsi space pada space f left parenthesis x right parenthesis end cell row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell turunan space pertama space fungsi space f left parenthesis x right parenthesis end cell row cell u apostrophe end cell equals cell turunan space pertama space fungsi space u end cell end table 

Misalkan u equals x minus x squared, maka:

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

Turunan pertama fungsi f open parentheses x close parentheses equals cube root of x minus x squared end root

 table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell cube root of u end cell row cell f open parentheses x close parentheses end cell equals cell u to the power of 1 third end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 1 third u to the power of 1 third minus 1 end exponent times u apostrophe end cell row blank equals cell 1 third u to the power of negative 2 over 3 end exponent times u apostrophe end cell row blank equals cell fraction numerator u apostrophe over denominator 3 u to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator u apostrophe over denominator 3 cube root of u squared end root end fraction end cell row blank equals cell fraction numerator 1 minus 2 x over denominator 3 cube root of open parentheses x minus x squared close parentheses squared end root end fraction end cell end table 

Jadi, turunan pertama fungsi f open parentheses x close parentheses equals cube root of x minus x squared end root adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus 2 x over denominator 3 cube root of open parentheses x minus x squared close parentheses squared end root end fraction end cell end table.

0

Roboguru

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