Jika f(x)=x2−x1​+1 maka f (x)= ...

Pertanyaan

Jika f open parentheses x close parentheses equals x squared minus 1 over x plus 1 maka f apostrophe open parentheses x close parentheses equals ...

  1. 2 x plus 1 over x squared

  2. x plus 1 over x squared

  3. x minus 1 over x squared plus 1

  4. 2 x minus 1 over x squared minus 1

  5. 2 x minus 1 over x squared

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Gunakan rumus turunan aljabar bentuk a x to the power of n, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell f apostrophe open parentheses x close parentheses end cell row cell a x to the power of n end cell equals cell n times a x to the power of n minus 1 end exponent end cell end table

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x squared minus 1 over x plus 1 end cell row cell f open parentheses x close parentheses end cell equals cell x squared minus x to the power of negative 1 end exponent plus 1 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 2 times x to the power of 2 minus 1 end exponent minus open parentheses negative 1 close parentheses times x to the power of negative 1 minus 1 end exponent plus 0 end cell row blank equals cell 2 x to the power of 1 minus open parentheses negative x close parentheses to the power of negative 2 end exponent end cell row blank equals cell 2 x plus x to the power of negative 2 end exponent end cell row blank equals cell 2 x plus 1 over x squared end cell end table

Maka f apostrophe open parentheses x close parentheses equals2 x plus 1 over x squared.

Jadi, jawaban yang tepat adalah A.

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