Roboguru

Tentukan turunan fungsi  menggunakan aturan

Pertanyaan

Tentukan turunan fungsi f left parenthesis x right parenthesis menggunakan aturan

 f apostrophe open parentheses x close parentheses equals limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction
f left parenthesis x right parenthesis equals x squared minus 5

 

Pembahasan Soal:

Turunan fungsi f left parenthesis x right parenthesis equals x squared minus 5 menggunakan aturan limit

 table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell limit as h rightwards arrow 0 of fraction numerator open parentheses open parentheses x plus h close parentheses squared minus 5 close parentheses minus open parentheses x squared minus 5 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open parentheses x squared plus 2 x h plus h squared minus 5 close parentheses minus open parentheses x squared minus 5 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x squared plus 2 x h plus h squared minus 5 minus x squared plus 5 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x h plus h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of 2 x plus h end cell row blank equals cell 2 x plus 0 end cell row blank equals cell 2 x end cell end table

Jadi, turunan fungsi f left parenthesis x right parenthesis equals x squared minus 5 adalah 2 x.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Umi

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Carilah turunan fungsi atau  dengan menggunakan pengertian dari turunan fungsi.

Pembahasan Soal:

Defisnisi turunan sebuah fungsi adalah nilai limit sebagai berikut:


f apostrophe left parenthesis x right parenthesis equals limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction


Maka, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator open parentheses left parenthesis x plus h right parenthesis squared plus 1 close parentheses minus open parentheses x squared plus 1 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x squared plus 2 x h plus h squared plus 1 minus x squared minus 1 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x h plus h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator up diagonal strike h left parenthesis 2 x plus h right parenthesis over denominator up diagonal strike h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of open parentheses 2 x plus h close parentheses end cell row blank equals cell 2 x plus 0 end cell row blank equals cell 2 x end cell end table


Jadi, turunan dari f left parenthesis x right parenthesis equals x squared plus 1 adalah f apostrophe left parenthesis x right parenthesis equals 2 x.

0

Roboguru

Tentukan persamaan garis singgung dan persamaan garis normal di titik dengan absis  pada setiap fungsi berikut. Petunjuk: carilah gradien persamaan garis singgung dengan menggunakan limit fungsi. a.

Pembahasan Soal:

Menentukan gradien persamaan garis singgung dengan menggunakan limit fungsi.

m equals limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction  

Persamaan garis singgung melalui titik open parentheses x subscript 1 comma space y subscript 1 close parentheses dengan gradien m adalah:

y minus y subscript 1 equals m open parentheses x minus x subscript 1 close parentheses 

Garis normal tegak lurus dengan garis singgung, maka persamaan garis normal adalah:

y minus y subscript 1 equals fraction numerator 1 over denominator negative m end fraction open parentheses x minus x subscript 1 close parentheses 

Diketahui f open parentheses x close parentheses equals 2 x melalui absis x equals 1, maka gradien garis singgung fungsi tersebut.

table attributes columnalign right center left columnspacing 0px end attributes row m equals cell limit as h rightwards arrow 0 of fraction numerator f open parentheses x plus h close parentheses minus f open parentheses x close parentheses over denominator h end fraction end cell row m equals cell limit as h rightwards arrow 0 of fraction numerator 2 open parentheses x plus h close parentheses minus 2 x over denominator h end fraction end cell row m equals cell limit as h rightwards arrow 0 of fraction numerator 2 x plus 2 h minus 2 x over denominator h end fraction end cell row m equals cell limit as h rightwards arrow 0 of fraction numerator 2 h over denominator h end fraction end cell row m equals cell limit as h rightwards arrow 0 of 2 end cell row m equals 2 row blank blank blank end table 

y equals f left parenthesis x right parenthesis, maka substitusikan x equals 1 pada f open parentheses x close parentheses equals 2 x untuk menentukan titik singgung.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f open parentheses x close parentheses end cell row y equals cell 2 x end cell row y equals cell 2 times 1 end cell row y equals 2 row blank blank cell therefore open parentheses 1 comma space 2 close parentheses end cell end table 

Persamaan garis singgung pada fungsi f open parentheses x close parentheses equals 2 x.

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell m open parentheses x minus x subscript 1 close parentheses end cell row cell y minus 2 end cell equals cell 2 open parentheses x minus 1 close parentheses end cell row y equals cell 2 x minus 2 plus 2 end cell row y equals cell 2 x end cell end table 

Persamaan garis normal pada fungsi f open parentheses x close parentheses equals 2 x.

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell fraction numerator 1 over denominator negative m end fraction open parentheses x minus x subscript 1 close parentheses end cell row cell y minus 2 end cell equals cell fraction numerator 1 over denominator negative 2 end fraction open parentheses x minus 1 close parentheses end cell row y equals cell negative 1 half x plus 1 half plus 2 end cell row y equals cell negative 1 half x plus 5 over 2 end cell end table 

Jadi, persamaan garis singgung dan persamaan garis normal fungsi f open parentheses x close parentheses equals 2 x berturut-turut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table (fungsi itu sendiri) dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell 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 cell 5 over 2 end cell end table.

0

Roboguru

Carilah turunan fungsi atau  dengan menggunakan pengertian dari turunan fungsi.

Pembahasan Soal:

Defisnisi turunan sebuah fungsi adalah nilai limit sebagai berikut:


f apostrophe left parenthesis x right parenthesis equals limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction


Maka, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 left parenthesis x plus h right parenthesis minus 5 minus open parentheses 2 x minus 5 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 x plus 2 h minus 5 minus 2 x plus 5 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 2 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of 2 end cell row blank equals 2 end table


Jadi, turunan dari f left parenthesis x right parenthesis equals 2 x minus 5 adalah f apostrophe left parenthesis x right parenthesis equals 2.

0

Roboguru

Dengan menggunakan definisi turunan fungsi aljabar, tentukan turunan dari fungsi !.

Pembahasan Soal:

Definisi turunan fungsi aljabar :

f apostrophe left parenthesis x right parenthesis equals limit as h rightwards arrow 0 of open parentheses fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction close parentheses

Dengan menggunakan definisi turunan fungsi aljabar, maka turunan dari fungsi f left parenthesis x right parenthesis equals 2 x minus 4 yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x minus 4 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of open parentheses fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction close parentheses end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of open parentheses fraction numerator 2 left parenthesis x plus h right parenthesis minus 4 minus left parenthesis 2 x minus 4 right parenthesis over denominator h end fraction close parentheses end cell row blank equals cell fraction numerator 2 x plus 2 h minus 4 minus 2 x plus 4 over denominator h end fraction end cell row blank equals cell fraction numerator 2 up diagonal strike h over denominator up diagonal strike h end fraction end cell row blank equals 2 end table

Jadi,  turunan dari fungsi f left parenthesis x right parenthesis equals 2 x minus 4 adalah 2.

1

Roboguru

Jika , maka tentukan  dengan menggunakan konsep limit!

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals 3 x minus 11.

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x plus h right parenthesis end cell equals cell 3 left parenthesis x plus h right parenthesis minus 11 end cell row blank equals cell 3 x plus 3 h minus 11 end cell end table 

Menentukan f apostrophe left parenthesis x right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 3 x plus 3 h minus 11 minus left parenthesis 3 x minus 11 right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 3 x minus 3 x plus 3 h minus 11 plus 11 over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 3 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space 3 end cell row blank equals 3 end table 

Jadi, f apostrophe left parenthesis x right parenthesis equals 3.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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