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Turunan pertama dari adalah f'(x). Nilai f'(1) =.....

Turunan pertama dari f left parenthesis x right parenthesis equals fraction numerator 3 x plus 5 over denominator x minus 2 end fraction comma x not equal to 2 adalah f'(x). Nilai f'(1) =....

  1. -11

  2. -6

  3. -5

  4. -3

  5. 17

Jawaban:

Bentuk fungsi

f left parenthesis x right parenthesis equals fraction numerator u left parenthesis x right parenthesis over denominator v left parenthesis x right parenthesis end fraction

Memiliki turunan pertama yang berbentuk

f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe left parenthesis x right parenthesis v left parenthesis x right parenthesis minus u left parenthesis x right parenthesis v apostrophe left parenthesis x right parenthesis over denominator v squared left parenthesis x right parenthesis end fraction

Jika

f left parenthesis x right parenthesis equals fraction numerator 3 x plus 5 over denominator x minus 2 end fraction maka

u left parenthesis x right parenthesis equals 3 x plus 5 rightwards arrow u apostrophe left parenthesis x right parenthesis equals 3  v left parenthesis x right parenthesis equals x minus 2 rightwards arrow v apostrophe left parenthesis x right parenthesis equals 1

Maka

f apostrophe left parenthesis x right parenthesis equals fraction numerator 3 left parenthesis x minus 2 right parenthesis minus 1 left parenthesis 3 x plus 5 right parenthesis over denominator left parenthesis x minus 2 right parenthesis squared end fraction  f apostrophe left parenthesis 1 right parenthesis equals fraction numerator 3 left parenthesis 1 minus 2 right parenthesis minus 1 left parenthesis 3 left parenthesis 1 right parenthesis plus 5 right parenthesis over denominator left parenthesis 1 minus 2 right parenthesis squared end fraction  f apostrophe left parenthesis 1 right parenthesis equals fraction numerator negative 3 minus 1 left parenthesis 8 right parenthesis over denominator left parenthesis negative 1 right parenthesis squared end fraction  f apostrophe left parenthesis 1 right parenthesis equals negative 11

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