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

Pertanyaan

Dengan menggunakan definisi turunan fungsi aljabar, tentukan turunan dari fungsi f left parenthesis x right parenthesis equals 2 minus 3 x plus x squared!

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 konsep limit, maka turunan dari fungsi f left parenthesis x right parenthesis equals 2 minus 3 x plus x squared yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 minus 3 x plus x squared 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 blank equals cell limit as h rightwards arrow 0 of open parentheses fraction numerator 2 minus 3 left parenthesis x plus h right parenthesis plus open parentheses x plus h close parentheses squared minus left parenthesis 2 minus 3 x plus x squared right parenthesis over denominator h end fraction close parentheses end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator up diagonal strike 2 up diagonal strike negative 3 end strike x minus 3 h up diagonal strike plus x squared end strike plus 2 x h plus h squared up diagonal strike negative 2 end strike up diagonal strike plus 3 x space end strike up diagonal strike negative x squared end strike over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator negative 3 h plus 2 x h plus h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator up diagonal strike h left parenthesis negative 3 plus 2 x plus h right parenthesis over denominator up diagonal strike h end fraction end cell row blank equals cell negative 3 plus 2 x plus 0 end cell row blank equals cell negative 3 x plus 2 x end cell end table

Jadi,  turunan dari fungsi f left parenthesis x right parenthesis equals 2 minus 3 x plus x squared adalah negative 3 x plus 2 x.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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