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.

$f (x) = x^{- 1}$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

turunan dari adalah .

turunan dari f left parenthesis x right parenthesis equals x to the power of negative 1 end exponent

adalah

f apostrophe left parenthesis x right parenthesis equals negative 1 over x squared

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:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator 1 over denominator left parenthesis x plus h right parenthesis end fraction end style minus begin display style 1 over x end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator begin display style fraction numerator x over denominator x left parenthesis x plus h right parenthesis end fraction minus fraction numerator left parenthesis x plus h right parenthesis over denominator x left parenthesis x plus h right parenthesis end fraction end style over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x minus left parenthesis x plus h right parenthesis over denominator x h left parenthesis x plus h right parenthesis end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator x minus x minus h over denominator x h left parenthesis x plus h right parenthesis end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator negative up diagonal strike h over denominator x up diagonal strike h left parenthesis x plus h right parenthesis end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator negative 1 over denominator x left parenthesis x plus h right parenthesis end fraction end cell row blank equals cell fraction numerator negative 1 over denominator x left parenthesis x plus 0 right parenthesis end fraction end cell row blank equals cell negative 1 over x squared end cell end table$

Jadi, turunan dari f left parenthesis x right parenthesis equals x to the power of negative 1 end exponent adalah f apostrophe left parenthesis x right parenthesis equals negative 1 over x squared .