Pertanyaan

Tentukan turunan fungsi menggunakan rumus f ( x ) = x → 0 lim h f ( x + h ) − f ( x ) a) f ( x ) = 2 x 3 + 5 x

Tentukan turunan fungsi menggunakan rumus

$f (x) = x \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$

a) $f (x) = 2 x^{3} + 5 x$

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

turunan fungsi adalah .

turunan fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x

adalah

f apostrophe left parenthesis x right parenthesis equals 6 x squared plus 5

Pembahasan

Diketahui fungsi . Turunan fungsi : Jadi, turunan fungsi adalah .

Diketahui fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x .

Turunan fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x :

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x cubed plus 5 x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 2 open parentheses x plus h close parentheses cubed plus 5 open parentheses x plus h close parentheses close parentheses minus open parentheses 2 x cubed plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 2 open parentheses x cubed plus 3 x squared h plus 3 x h squared plus h cubed close parentheses plus 5 x plus 5 h close parentheses minus open parentheses 2 x cubed plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator open parentheses 2 x cubed plus 6 x squared h plus 6 x h squared plus 2 h cubed plus 5 x plus 5 h close parentheses minus open parentheses 2 x cubed plus 5 x close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator 6 x squared h plus 6 x h squared plus 2 h cubed plus 5 h over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space fraction numerator h open parentheses 6 x squared plus 6 x h plus 2 h squared plus 5 close parentheses over denominator h end fraction end cell row blank equals cell limit as h rightwards arrow 0 of space 6 x squared plus 6 x h plus 2 h squared plus 5 end cell row blank equals cell 6 x squared plus 6 x open parentheses 0 close parentheses plus 2 open parentheses 0 close parentheses squared plus 5 end cell row blank equals cell 6 x squared plus 5 end cell end table end style$

Jadi, turunan fungsi f open parentheses x close parentheses equals 2 x cubed plus 5 x adalah f apostrophe left parenthesis x right parenthesis equals 6 x squared plus 5 .