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Turunan pertama dari adalah ....

Pertanyaan

Turunan pertama dari begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator straight x squared plus straight x minus 1 over denominator 3 straight x squared plus straight x plus 5 end fraction blank end style adalah ....

  1. begin mathsize 14px style fraction numerator negative 2 straight x squared plus 16 straight x plus 6 over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end style

  2. begin mathsize 14px style fraction numerator 2 straight x squared plus 16 straight x minus 6 over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end style

  3. begin mathsize 14px style fraction numerator straight x squared plus 16 straight x minus 6 over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end style

  4. begin mathsize 14px style fraction numerator negative 2 straight x squared plus 16 straight x minus 6 over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end style

  5. begin mathsize 14px style fraction numerator negative 2 straight x squared minus 16 straight x minus 6 over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end style

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Ingat kembali turunan pertama fungsi dalam irasional berikut ini

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adalah

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Sehingga pada fungsi irasional berikut ini

begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator straight x squared plus straight x minus 1 over denominator 3 straight x squared plus straight x plus 5 end fraction end style 

Kita misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight u left parenthesis straight x right parenthesis end cell equals cell straight x squared plus straight x minus 1 end cell row cell straight v left parenthesis straight x right parenthesis end cell equals cell 3 straight x squared plus straight x plus 5 end cell end table end style

Maka diperoleh,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight u to the power of straight apostrophe open parentheses straight x close parentheses end cell equals cell 2 straight x plus 1 end cell row cell straight v to the power of straight apostrophe open parentheses straight x close parentheses end cell equals cell 6 straight x plus 1 end cell end table end style 

Sehingga turunan pertama fungsi tersebut adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f to the power of straight apostrophe open parentheses straight x close parentheses end cell equals cell fraction numerator open parentheses 2 straight x plus 1 close parentheses open parentheses 3 straight x squared plus straight x plus 5 blank close parentheses minus open parentheses straight x squared plus straight x minus 1 close parentheses open parentheses 6 straight x plus 1 close parentheses over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 6 straight x cubed plus 5 straight x squared plus 11 straight x plus 5 close parentheses minus open parentheses 6 straight x cubed plus 7 straight x squared minus 5 straight x minus 1 close parentheses over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 2 straight x squared plus 16 straight x plus 6 over denominator open parentheses 3 straight x squared plus straight x plus 5 close parentheses squared end fraction end cell end table end style 

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