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Pertanyaan

Jika f open parentheses x close parentheses equals fraction numerator x squared minus 3 x over denominator x squared plus 2 x plus 1 end fraction. Tentukan f apostrophe open parentheses 2 close parentheses.

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Untuk menyelesaikan soal tersebut terlebih dahulu dicari turunan fungsi rasional tersebut kemudian disubstitusi nilai x = 2 ke dalam fungsi turunan yang diperoleh.

Misalkan:

u equals x squared minus 3 x space rightwards arrow space u apostrophe equals 2 x minus 3 

v equals x squared plus 2 x plus 1 space rightwards arrow space v apostrophe equals 2 x plus 2 

blank table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator v times u apostrophe minus u times v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses x squared plus 2 x plus 1 close parentheses open parentheses 2 x minus 3 close parentheses minus open parentheses x squared minus 3 x close parentheses open parentheses 2 x plus 2 close parentheses over denominator open parentheses x squared plus 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 x cubed minus 3 x squared plus 4 x squared minus 6 x plus 2 x minus 3 close parentheses minus open parentheses 2 x cubed plus 2 x squared minus 6 x squared minus 6 x close parentheses over denominator open parentheses open parentheses x plus 1 close parentheses squared close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x cubed plus x squared minus 4 x minus 3 minus open parentheses 2 x cubed minus 4 x squared minus 6 x close parentheses over denominator open parentheses x plus 1 close parentheses to the power of 4 end fraction end cell row blank equals cell fraction numerator 2 x cubed plus x squared minus 4 x minus 3 minus 2 x cubed plus 4 x squared plus 6 x over denominator open parentheses x plus 1 close parentheses to the power of 4 end fraction end cell row blank equals cell fraction numerator 5 x squared plus 2 x minus 3 over denominator open parentheses x plus 1 close parentheses to the power of 4 end fraction end cell row blank equals cell fraction numerator open parentheses 5 x minus 3 close parentheses open parentheses x plus 1 close parentheses over denominator open parentheses x plus 1 close parentheses to the power of 4 end fraction end cell row blank equals cell fraction numerator open parentheses 5 x minus 3 close parentheses over denominator open parentheses x plus 1 close parentheses cubed end fraction end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses 2 close parentheses end cell equals cell fraction numerator 5 open parentheses 2 close parentheses minus 3 over denominator open parentheses 5 plus 1 close parentheses cubed end fraction end cell row blank equals cell fraction numerator 10 minus 3 over denominator 6 cubed end fraction end cell row blank equals cell 7 over 216 end cell end table 

Dengan demikian, hasil dari f apostrophe open parentheses 2 close parentheses equals 7 over 216.

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