Pertanyaan

Tentukan nilai turunan fungsi untuk nilai x yang diberikan dari fungsi-fungsi berikut! a. f ( x ) = 7 x + 2 2 x + 1 , x = 1

Tentukan nilai turunan fungsi untuk nilai $x$ yang diberikan dari fungsi-fungsi berikut!

a. $f (x) = \frac{2 x + 1}{7 x + 2}, x = 1$

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai turunan fungsi adalah .

nilai turunan fungsi $f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator square root of 7 x plus 2 end root end fraction comma space x equals 1$ adalah negative 1 over 9

Pembahasan

Diketahui: Misalkan: Turunan dari fungsi : Nilai dari turunan fungsi jika : Jadi,nilai turunan fungsi adalah .

Diketahui:

$f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator square root of 7 x plus 2 end root end fraction comma space x equals 1$

Misalkan:

u equals 2 x plus 1 rightwards arrow u apostrophe equals 2 v equals square root of 7 x plus 2 end root equals open parentheses 7 x plus 2 close parentheses to the power of 1 half end exponent rightwards arrow v apostrophe equals 7 times 1 half open parentheses 7 x plus 2 close parentheses to the power of negative 1 half end exponent

Turunan dari fungsi $f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator square root of 7 x plus 2 end root end fraction$ :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 1 over denominator square root of 7 x plus 2 end root end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 7 x plus 2 end root close parentheses minus begin display style fraction numerator 7 over denominator 2 square root of 7 x plus 2 end root end fraction end style over denominator open parentheses square root of 7 x plus 2 end root close parentheses squared end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator open parentheses 2 square root of 7 x plus 2 end root close parentheses squared minus 7 open parentheses 2 square root of 7 x plus 2 end root close parentheses over denominator 2 square root of 7 x plus 2 end root end fraction end style over denominator 7 x plus 2 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 4 open parentheses 7 x plus 2 close parentheses minus 14 square root of 7 x plus 2 end root over denominator 2 square root of 7 x plus 2 end root end fraction end style over denominator 7 x plus 2 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 left parenthesis 7 x plus 2 right parenthesis minus 7 square root of 7 x plus 2 end root over denominator square root of 7 x plus 2 end root end fraction end style over denominator 7 x plus 2 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 7 x plus 2 close parentheses minus 7 square root of 7 x plus 2 end root over denominator square root of 7 x plus 2 end root end fraction cross times fraction numerator 1 over denominator 7 x plus 2 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 7 x plus 2 close parentheses minus 7 square root of 7 x plus 2 end root over denominator open parentheses 7 x plus 2 close parentheses square root of 7 x plus 2 end root end fraction end cell end table$

Nilai dari turunan fungsi $f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator square root of 7 x plus 2 end root end fraction$ jika x equals 1 :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 2 open parentheses 7 x plus 2 close parentheses minus 7 square root of 7 x plus 2 end root over denominator open parentheses 7 x plus 2 close parentheses square root of 7 x plus 2 end root end fraction end cell row cell f apostrophe left parenthesis 1 right parenthesis end cell equals cell fraction numerator 2 open parentheses 7 plus 2 close parentheses minus 7 square root of 7 plus 2 end root over denominator open parentheses 7 plus 2 close parentheses square root of 7 plus 2 end root end fraction end cell row blank equals cell fraction numerator 2 open parentheses 9 close parentheses minus 7 square root of 9 over denominator 9 square root of 9 end fraction end cell row blank equals cell fraction numerator 18 minus 7 open parentheses 3 close parentheses over denominator 9 open parentheses 3 close parentheses end fraction end cell row blank equals cell fraction numerator 18 minus 21 over denominator 27 end fraction end cell row blank equals cell negative 3 over 27 end cell row blank equals cell negative 1 over 9 end cell end table$

Jadi, nilai turunan fungsi $f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator square root of 7 x plus 2 end root end fraction comma space x equals 1$ adalah negative 1 over 9 .