Pertanyaan

Tentukan turunan pertama fungsi berikut dengan menggunakan aturan turunan (penjumlahan, pengurangan, perkalian, pembagian, dan aturan rantai turunan) e. f ( x ) = 2 x 2 − 1 x + 2

Tentukan turunan pertama fungsi berikut dengan menggunakan aturan turunan (penjumlahan, pengurangan, perkalian, pembagian, dan aturan rantai turunan)

e. $f (x) = \frac{x + 2}{2 x ^{2} - 1}$

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

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$table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 2 x squared plus 9 close parentheses over denominator open parentheses 2 x squared minus 1 close parentheses squared end fraction end cell end table$ .

Pembahasan

Rumus turunan fungsi bentuk pembagian adalah sebagai berikut Diketahui Sehingga diperoleh Dengan demikian .

Rumus turunan fungsi bentuk pembagian adalah sebagai berikut

$f open parentheses x close parentheses equals U over V rightwards arrow f apostrophe open parentheses x close parentheses equals fraction numerator U apostrophe V minus U V apostrophe over denominator V squared end fraction$

Diketahui

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x plus 2 over denominator 2 x squared minus 1 end fraction end cell row U equals cell x plus 2 rightwards arrow U apostrophe equals 1 end cell row V equals cell 2 x squared minus 1 rightwards arrow V apostrophe equals 4 x end cell end table$

Sehingga diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator U apostrophe V minus U V apostrophe over denominator V squared end fraction end cell row blank equals cell fraction numerator 1 times open parentheses 2 x squared minus 1 close parentheses minus open parentheses x plus 2 close parentheses times open parentheses 4 x close parentheses over denominator open parentheses 2 x squared minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x squared minus 1 minus 4 x squared minus 8 over denominator open parentheses 2 x squared minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 2 x squared minus 9 over denominator open parentheses 2 x squared minus 1 close parentheses squared end fraction end cell row blank equals cell negative fraction numerator open parentheses 2 x squared plus 9 close parentheses over denominator open parentheses 2 x squared minus 1 close parentheses squared end fraction end cell end table$

Dengan demikian $table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator open parentheses 2 x squared plus 9 close parentheses over denominator open parentheses 2 x squared minus 1 close parentheses squared end fraction end cell end table$ .