Pertanyaan

Carilah turunan fungsi atau f ( x ) dengan menggunakan pengertian dari turunan fungsi. f ( x ) = x 1

Carilah turunan fungsi atau $f (x)$ dengan menggunakan pengertian dari turunan fungsi.

$f (x) = \frac{1}{x}$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

turunan dari adalah .

turunan dari $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction$ adalah $f apostrophe left parenthesis x right parenthesis equals negative fraction numerator 1 over denominator 2 x square root of x end fraction$ .

Pembahasan

Defisnisi turunan sebuah fungsi adalah nilai limit sebagai berikut: Maka, diperoleh: Jadi, turunan dari adalah .

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 begin display style fraction numerator 1 over denominator square root of x plus h end root end fraction end style minus begin display style fraction numerator 1 over denominator square root of x end fraction end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator fraction numerator square root of x minus square root of x plus h end root over denominator square root of x square root of x plus h end root end fraction over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator square root of x minus square root of x plus h end root over denominator h square root of x square root of x plus h end root end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator square root of x minus square root of x plus h end root over denominator h square root of x square root of x plus h end root end fraction cross times fraction numerator square root of x plus square root of x plus h end root over denominator square root of x plus square root of x plus h end root end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x minus open parentheses x plus h close parentheses over denominator h square root of x square root of x plus h end root times open parentheses square root of x plus square root of x plus h end root close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator negative up diagonal strike h over denominator up diagonal strike h square root of x square root of x plus h end root times open parentheses square root of x plus square root of x plus h end root close parentheses end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator negative 1 over denominator square root of x square root of x plus h end root times open parentheses square root of x plus square root of x plus h end root close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator square root of x square root of x plus 0 end root times open parentheses square root of x plus square root of x plus 0 end root close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator square root of x square root of x times open parentheses square root of x plus square root of x close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator x times 2 square root of x end fraction end cell row blank equals cell negative fraction numerator 1 over denominator 2 x square root of x end fraction end cell end table$

Jadi, turunan dari $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction$ adalah $f apostrophe left parenthesis x right parenthesis equals negative fraction numerator 1 over denominator 2 x square root of x end fraction$ .