Pertanyaan

Diketahui f ( x ) = 3 x − 4 2 x − 5 dan f'(x) adalah turunan pertama dari f(x). Nilai dari f'(1) = ........

Diketahui $f (x) = \frac{2 x - 5}{3 x - 4}$ dan f'(x) adalah turunan pertama dari f(x). Nilai dari f'(1) = ........

-22
-12
-7
7
22

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Sehingga Untuk x = 1, didapat

$f left parenthesis x right parenthesis equals u over v rightwards double arrow f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe. v minus u. v apostrophe over denominator v squared end fraction$

Sehingga

$u equals 2 x minus 5 rightwards arrow u apostrophe equals 2 v equals 3 x minus 4 rightwards arrow v apostrophe equals 3 f left parenthesis x right parenthesis equals fraction numerator 2 x minus 5 over denominator 3 x minus 4 end fraction rightwards arrow f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe. v minus u. v apostrophe over denominator v squared end fraction equals fraction numerator 2 left parenthesis 3 x minus 4 right parenthesis minus left parenthesis 2 x minus 5 right parenthesis 3 over denominator left parenthesis 3 x minus 4 right parenthesis squared end fraction equals fraction numerator left parenthesis 6 x minus 8 right parenthesis left parenthesis 6 x minus 15 right parenthesis over denominator left parenthesis 3 x minus 4 right parenthesis squared end fraction equals fraction numerator 7 over denominator left parenthesis 3 x minus 4 right parenthesis squared end fraction$

Untuk x = 1, didapat

$f apostrophe left parenthesis 1 right parenthesis equals fraction numerator 7 over denominator left parenthesis 3 left parenthesis 1 right parenthesis minus 4 right parenthesis squared end fraction equals fraction numerator 7 over denominator left parenthesis negative 1 right parenthesis squared end fraction equals 7$