Buktikan bahwa turunan dari f(x)=16x2 adalah 32x.

Pertanyaan

Buktikan bahwa turunan dari $f(x)=16x^2$ adalah $32x$ .

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

terbukti bahwa turunan dari f left parenthesis x right parenthesis equals 16 x squared

adalah

Pembahasan

Defisnisi turunan sebuah fungsi adalah nilai limit sebagai berikut:

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

Maka, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as x rightwards arrow 0 of fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 16 left parenthesis x plus h right parenthesis squared minus 16 x squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 16 open parentheses x squared plus 2 x h plus h squared close parentheses minus 16 x squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 16 x squared plus 32 x h plus h squared minus 16 x squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator 32 x h plus 16 h squared over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of fraction numerator up diagonal strike h open parentheses 32 x plus 16 h close parentheses over denominator up diagonal strike h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of left parenthesis 32 x plus 16 h right parenthesis end cell row blank equals cell 32 x plus 16 times 0 end cell row blank equals cell 32 x end cell end table$

Jadi, terbukti bahwa turunan dari f left parenthesis x right parenthesis equals 16 x squared adalah 32 x .