Pertanyaan

$Diketahui space f left parenthesis x right parenthesis space equals fraction numerator 2 x space long dash 5 over denominator 3 x minus 4 end fraction space dan space f space apostrophe space left parenthesis x right parenthesis space adalah space turunan space pertama space dari space f left parenthesis x right parenthesis. space Nilai space dari space f apostrophe left parenthesis 1 right parenthesis equals... space space$

-22
-12
-7
7
22

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

$Fungsi space turunan space f left parenthesis x right parenthesis equals u over v space memiliki space fungsi space turunan space f to the power of apostrophe left parenthesis x right parenthesis equals fraction numerator u to the power of apostrophe times v minus u times v to the power of apostrophe over denominator v squared end fraction Sehingga space f left parenthesis x right parenthesis equals fraction numerator 2 x minus 5 over denominator 3 x minus 4 end fraction u equals 2 x minus 5 rightwards arrow u to the power of apostrophe equals 2 v equals 3 x minus 4 rightwards arrow v to the power of apostrophe equals 3 f to the power of apostrophe left parenthesis x right parenthesis equals fraction numerator 2 left parenthesis 3 x minus 4 right parenthesis minus left parenthesis 2 x minus 5 right parenthesis 3 over denominator left parenthesis 3 x minus 4 right parenthesis squared end fraction space space space space space space space space equals fraction numerator left parenthesis 6 x minus 8 right parenthesis minus left parenthesis 6 x minus 15 right parenthesis over denominator left parenthesis 3 x minus 4 right parenthesis squared end fraction space space space space space space space space equals fraction numerator 7 over denominator left parenthesis 3 x minus 4 right parenthesis squared end fraction Untuk space straight x equals 1 comma space diperoleh f to the power of apostrophe left parenthesis 1 right parenthesis equals fraction numerator 7 over denominator left parenthesis 3 left parenthesis 1 right parenthesis minus 4 right parenthesis squared end fraction equals fraction numerator 7 over denominator left parenthesis negative 1 right parenthesis squared end fraction equals 7$