Roboguru

Dengan menggunakan rumus turunan untuk fungsi , yaitu , carilah turunan dari tiap fungsi berikut ini. h.

Pertanyaan

Dengan menggunakan rumus turunan untuk fungsi f left parenthesis x right parenthesis equals open curly brackets u open parentheses x close parentheses close curly brackets to the power of n, yaitu f apostrophe open parentheses x close parentheses equals n open curly brackets u open parentheses x close parentheses close curly brackets to the power of n minus 1 end exponent times u apostrophe open parentheses n close parentheses, carilah turunan dari tiap fungsi berikut ini.

h. f open parentheses x close parentheses equals open parentheses x squared minus 4 x squared close parentheses to the power of negative 1 fourth end exponent

Pembahasan Soal:

Dengan menggunakan rumus turunan bentuk f apostrophe open parentheses x close parentheses equals n open curly brackets u open parentheses x close parentheses close curly brackets to the power of n minus 1 end exponent times u apostrophe open parentheses n close parentheses  maka:

 f open parentheses x close parentheses equals open parentheses x squared minus 4 x squared close parentheses to the power of negative 1 fourth end exponent f apostrophe open parentheses x close parentheses equals negative 1 fourth open parentheses x squared minus 4 x squared close parentheses to the power of negative 5 over 4 end exponent open parentheses 2 x minus 4 close parentheses f apostrophe open parentheses x close parentheses equals open parentheses negative 1 half x plus 1 close parentheses open parentheses x squared minus 4 x squared close parentheses to the power of negative 5 over 4 end exponent

Jadi, turunan dari fungsi tersebut adalah f apostrophe open parentheses x close parentheses equals open parentheses negative 1 half x plus 1 close parentheses open parentheses x squared minus 4 x squared close parentheses to the power of negative 5 over 4 end exponent

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Nasrullah

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan  jika diketahui fungsi-fungsi berikut. c.  .

Pembahasan Soal:

Diberikan suatu fungsi: size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 3 size 14px x size 14px plus size 14px 5 size 14px right parenthesis to the power of size 14px 2 over size 14px 3 end exponent

Turunan pertama dapat ditentukan dengan menerapkan aturan rantai.

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 2 over 3 open parentheses negative 3 x plus 5 close parentheses to the power of 2 over 3 minus 1 end exponent times open parentheses negative 3 close parentheses end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell negative 2 open parentheses negative 3 x plus 5 close parentheses to the power of negative 1 third end exponent end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell negative fraction numerator 2 over denominator cube root of negative 3 x plus 5 end root end fraction end cell row blank blank blank end table end style 

Jadi, turunan pertama fungsi tersebut adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell bottom enclose bold minus fraction numerator bold 2 over denominator root index bold 3 of bold minus bold 3 bold x bold plus bold 5 end root end fraction end enclose end cell end table end style.

0

Roboguru

Dengan menggunakan konsep turunan, tentukan turunan dari fungsi-fungsi berikut.

Pembahasan Soal:

Informasi penting: begin mathsize 14px style square root of x equals x to the power of 1 half end exponent end style

Misal

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 2 x cubed minus 1 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 6 x squared end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f open parentheses x close parentheses equals u to the power of 1 half end exponent end cell row cell fraction numerator d y over denominator d u end fraction end cell equals cell 1 half u to the power of negative 1 half end exponent end cell row blank equals cell fraction numerator 1 over denominator 2 u to the power of 1 half end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 square root of u end fraction end cell end table end style

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 square root of u end fraction times 6 x squared end cell row blank equals cell fraction numerator 3 x squared over denominator square root of 2 x cubed minus 1 end root end fraction end cell end table end style

Jadi turunan dari begin mathsize 14px style square root of 2 x cubed minus 1 end root end style adalah begin mathsize 14px style fraction numerator 3 x squared over denominator square root of 2 x cubed minus 1 end root end fraction end style

0

Roboguru

Turunan pertama dari adalah

Pembahasan Soal:

Apabila terdapat g left parenthesis x right parenthesis equals a x to the power of n maka turunan pertamanya adalah g apostrophe left parenthesis x right parenthesis equals a. n. x to the power of n minus 1 end exponent.

Diketahui: f left parenthesis x right parenthesis equals 6 x cubed minus 4 x squared plus 3 x plus 7

Ditanya: f apostrophe left parenthesis x right parenthesis ?

Jawab:

f apostrophe left parenthesis x right parenthesis equals 6.3 x to the power of 3 minus 1 end exponent minus 4.2 x to the power of 2 minus 1 end exponent plus 3 x to the power of 1 minus 1 end exponent f apostrophe left parenthesis x right parenthesis equals 18 x squared minus 8 x plus 3

Jadi, turunan pertamanya adalah f apostrophe left parenthesis x right parenthesis equals 18 x squared minus 8 x plus 3.

0

Roboguru

Tentukan turunan fungsi menggunakan rumus    a)

Pembahasan Soal:

Diketahui fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x.

Turunan fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x cubed plus 5 x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 2 open parentheses x plus h close parentheses cubed plus 5 open parentheses x plus h close parentheses close parentheses minus open parentheses 2 x cubed plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 2 open parentheses x cubed plus 3 x squared h plus 3 x h squared plus h cubed close parentheses plus 5 x plus 5 h close parentheses minus open parentheses 2 x cubed plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 2 x cubed plus 6 x squared h plus 6 x h squared plus 2 h cubed plus 5 x plus 5 h close parentheses minus open parentheses 2 x cubed plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 6 x squared h plus 6 x h squared plus 2 h cubed plus 5 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator h open parentheses 6 x squared plus 6 x h plus 2 h squared plus 5 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space 6 x squared plus 6 x h plus 2 h squared plus 5 end cell row blank equals cell 6 x squared plus 6 x open parentheses 0 close parentheses plus 2 open parentheses 0 close parentheses squared plus 5 end cell row blank equals cell 6 x squared plus 5 end cell end table end style 

Jadi, turunan fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x adalah f apostrophe left parenthesis x right parenthesis equals 6 x squared plus 5.

0

Roboguru

Diketahui fungsi . Tentukan turunan pertama fungsi .

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 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.

0

Roboguru

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