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Diketahui fungsi . Turunan pertama fungsi f(x) ada...

Diketahui fungsi begin mathsize 12px style f left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator 3 x minus 1 end fraction end style. Turunan pertama fungsi f(x) adalah f'(x).

Nilai dari f'(1)= ...

  1. negative 3

  2. 1 fourth

  3. 1 half

  4. 2 over 3

  5. 5 over 2

Jawaban:

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

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