Pertanyaan

Turunan pertama dari fungsi adalah ...

$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals 4 x open parentheses ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus fraction numerator x minus 2 over denominator x squared minus 4 x plus 3 end fraction close parentheses end style$
$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals 4 x open parentheses ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus fraction numerator x squared minus 2 x over denominator x squared minus 4 x plus 3 end fraction close parentheses end style$
$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals 4 x open parentheses ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus fraction numerator x cubed minus 4 x squared plus 3 x over denominator x minus 2 end fraction close parentheses end style$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Misalkan u(x) = 2x dan v(x) = ln⁡(x - 4x + 3). Berdasarkan turunan aljabar, didapat u' (x) = 4x. Kemudian perhatikan v(x). Misalkan g(x) = x - 4x + 3, maka didapat g' (x) = 2x - 4. Oleh karena itu, Kemudian, Jadi, jawaban yang tepat adalah D.

Misalkan u(x) = 2x dan v(x) = ln⁡(x - 4x + 3).

Berdasarkan turunan aljabar, didapat u' (x) = 4x.

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell v open parentheses x close parentheses end cell equals cell ln invisible function application open parentheses x squared minus 4 x plus 4 close parentheses end cell row cell v open parentheses x close parentheses end cell equals cell ln invisible function application g open parentheses x close parentheses end cell row cell v to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator g open parentheses x close parentheses end fraction times g to the power of apostrophe open parentheses x close parentheses end cell row cell v to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator x squared minus 4 x plus 3 end fraction times open parentheses 2 x minus 4 close parentheses end cell row cell v to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 x minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell end table end style$

Kemudian perhatikan v(x).

Misalkan g(x) = x - 4x + 3, maka didapat g' (x) = 2x - 4.

Oleh karena itu,

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x squared ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses end cell row cell f open parentheses x close parentheses end cell equals cell u open parentheses x close parentheses v open parentheses x close parentheses end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell u to the power of apostrophe open parentheses x close parentheses v open parentheses x close parentheses plus u open parentheses x close parentheses v to the power of apostrophe open parentheses x close parentheses end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 4 x times ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus 2 x squared times fraction numerator 2 x minus 4 over denominator x squared minus 4 x plus 3 end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 4 x times ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus 2 x squared times fraction numerator 2 open parentheses x minus 2 close parentheses over denominator x squared minus 4 x plus 3 end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 4 x times ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus 4 x squared times fraction numerator x minus 2 over denominator x squared minus 4 x plus 3 end fraction end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 4 x open parentheses ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus x times fraction numerator x minus 2 over denominator x squared minus 4 x plus 3 end fraction close parentheses end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 4 x open parentheses ln invisible function application open parentheses x squared minus 4 x plus 3 close parentheses plus fraction numerator x squared minus 2 x over denominator x squared minus 4 x plus 3 end fraction close parentheses end cell end table end style$

Kemudian,

Jadi, jawaban yang tepat adalah D.