Pertanyaan

Turunan pertama f ( x ) = 3 x − 1 x 2 + 1 adalah f ( x ) = ...

Turunan pertama $f (x) = \frac{x ^{2} + 1}{3 x - 1}$ adalah $f (x) = ...$

$fraction numerator 3 x squared minus 2 x minus 3 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction$
$fraction numerator 3 x squared minus 2 x plus 3 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction$
$fraction numerator 3 x squared minus 2 x minus 2 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction$
$fraction numerator 9 x squared minus 2 x minus 3 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction$
$fraction numerator 9 x squared minus 2 x plus 3 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Diketahui: Ditanya: ? Jawab: Konsep: Misalkan Maka, Oleh karena itu, jawaban yang benar adalah A.

Diketahui: $f left parenthesis x right parenthesis equals fraction numerator x squared plus 1 over denominator 3 x minus 1 end fraction$

Ditanya: f apostrophe left parenthesis x right parenthesis ?

Jawab:

Konsep: $g left parenthesis x right parenthesis equals u over v rightwards arrow g apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction$

Misalkan

u equals x squared plus 1 rightwards arrow u apostrophe equals 2 x v equals 3 x minus 1 rightwards arrow v apostrophe equals 3

Maka,

$f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction f apostrophe left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x close parentheses open parentheses 3 x minus 1 close parentheses minus open parentheses 3 close parentheses open parentheses x squared plus 1 close parentheses over denominator open parentheses 3 x minus 1 close parentheses squared end fraction f apostrophe left parenthesis x right parenthesis equals fraction numerator 6 x squared minus 2 x minus 3 x squared minus 3 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction f apostrophe left parenthesis x right parenthesis equals fraction numerator 3 x squared minus 2 x minus 3 over denominator open parentheses 3 x minus 1 close parentheses squared end fraction$

Oleh karena itu, jawaban yang benar adalah A.