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Pertanyaan

Diketahui f left parenthesis x right parenthesis equals fraction numerator 2 x minus 5 over denominator 3 x minus 4 end fraction dan f'(x) adalah turunan pertama dari f(x). Nilai dari f'(1) = ........

  1. -22

  2. -12

  3. -7

  4. 7

  5. 22

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

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

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