Pertanyaan

Diketahui fungsi f ( x ) = 3 x − 1 2 x − 1 . Turunan pertama fungsi f ( x ) adalah f' ( x ). Nilai dari f' (1)= ...

Diketahui fungsi $f (x) = \frac{2 x - 1}{3 x - 1}$ . Turunan pertama fungsi f(x) adalah f'(x).

Nilai dari f'(1)= ...

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$Ingat space rumus space berikut space ini factorial straight f left parenthesis straight x right parenthesis equals fraction numerator straight u left parenthesis straight x right parenthesis over denominator straight v left parenthesis straight x right parenthesis end fraction straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator straight u apostrophe left parenthesis straight x right parenthesis straight v left parenthesis straight x right parenthesis minus straight u left parenthesis straight x right parenthesis straight v apostrophe left parenthesis straight x right parenthesis over denominator left parenthesis straight v left parenthesis straight x right parenthesis right parenthesis squared end fraction straight f left parenthesis straight x right parenthesis equals fraction numerator 2 straight x minus 1 over denominator 3 straight x minus 1 end fraction dengan space space straight u left parenthesis straight x right parenthesis equals 2 straight x minus 1 space rightwards double arrow straight u apostrophe left parenthesis straight x right parenthesis equals 2 space space space space space space space space space space space space space space space straight v left parenthesis straight x right parenthesis equals 3 straight x minus 1 rightwards double arrow space straight v apostrophe left parenthesis straight x right parenthesis equals 3 maka space turunan space fungsi space tersebut space menjadi space colon straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator 2 left parenthesis 3 straight x minus 1 right parenthesis minus left parenthesis 2 straight x minus 1 right parenthesis left parenthesis 3 right parenthesis over denominator left parenthesis 3 straight x minus 1 right parenthesis squared end fraction untuk space straight x equals 1 space diperoleh space colon straight f apostrophe left parenthesis 1 right parenthesis equals fraction numerator 2 left parenthesis 3 left parenthesis 1 right parenthesis minus 1 right parenthesis minus left parenthesis 2 left parenthesis 1 right parenthesis minus 1 right parenthesis left parenthesis 3 right parenthesis over denominator left parenthesis 3 left parenthesis 1 right parenthesis minus 1 right parenthesis squared end fraction equals 1 fourth$