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Pertanyaan

Diketahuif open parentheses x close parentheses equals fraction numerator x minus 4 over denominator 3 x plus 2 end fraction semicolon x not equal to negative 2 over 3 dan f to the power of apostrophe open parentheses x close parentheses merupakan turunan pertama f open parentheses x close parentheses. Nilai f to the power of apostrophe open parentheses negative 1 close parentheses equals space...

  1. 14

  2. 10

  3. 8

  4. -10

  5. -14

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

Ingat kembali aturan turunan berikut ini :

f open parentheses x close parentheses equals fraction numerator u open parentheses x close parentheses over denominator v open parentheses x close parentheses end fraction rightwards double arrow f to the power of apostrophe open parentheses x close parentheses equals fraction numerator u to the power of apostrophe open parentheses x close parentheses space v open parentheses x close parentheses minus u open parentheses x close parentheses space v to the power of apostrophe open parentheses x close parentheses over denominator open parentheses v open parentheses x close parentheses close parentheses squared end fraction

Misalkan :

u open parentheses x close parentheses equals x minus 4 rightwards double arrow u to the power of apostrophe open parentheses x close parentheses equals 1  v open parentheses x close parentheses equals 3 x plus 2 rightwards double arrow v to the power of apostrophe open parentheses x close parentheses equals 3

Sehingga,

f to the power of apostrophe open parentheses x close parentheses equals fraction numerator open parentheses 1 close parentheses open parentheses 3 x plus 2 close parentheses minus open parentheses x minus 4 close parentheses open parentheses 3 close parentheses over denominator open parentheses 3 x plus 2 close parentheses squared end fraction  f to the power of apostrophe open parentheses x close parentheses equals 14 over open parentheses 3 x plus 2 close parentheses squared

Untuk x equals negative 1 , maka :

f to the power of apostrophe open parentheses x close parentheses equals 14 over open parentheses 3 open parentheses negative 1 close parentheses plus 2 close parentheses squared equals 14 over open parentheses negative 1 close parentheses squared equals 14

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