Pertanyaan

Turunan pertama dari fungsi adalah ....

$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 15 x squared over denominator x cubed plus 2 end fraction plus 2 sin invisible function application 2 x end style$
$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 15 x squared over denominator x cubed plus 2 end fraction minus 2 sin invisible function application 2 x end style$
$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 3 x squared over denominator x cubed plus 2 end fraction plus 2 sin invisible function application 2 x end style$
$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 15 x squared over denominator x cubed plus 2 end fraction minus sin invisible function application 2 x end style$
$begin mathsize 12px style f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 15 x squared over denominator x cubed plus 2 end fraction plus sin invisible function application 2 x end style$

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 A.

Pembahasan

Misalkan g(x) = ln (x + 2) dan h(x) = cos ⁡2x. Berdasarkan turunan trigonometri, didapat h' (x) = -2 sin ⁡2x. Kemudian, perhatikan g(x). Misalkan u(x) = (x + 2) . Berdasarkan aturan rantai, didapat Oleh karena itu Kemudian, didapat Jadi, jawaban yang tepat adalah A.

Misalkan g(x) = ln (x + 2) dan h(x) = cos ⁡2x.

Berdasarkan turunan trigonometri, didapat h' (x) = -2 sin ⁡2x.

Kemudian, perhatikan g(x).

Misalkan u(x) = (x + 2). Berdasarkan aturan rantai, didapat

Oleh karena itu

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell ln invisible function application open parentheses x cubed plus 2 close parentheses to the power of 5 end cell row cell g open parentheses x close parentheses end cell equals cell ln invisible function application u open parentheses x close parentheses end cell row cell g to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator u open parentheses x close parentheses end fraction times u to the power of apostrophe open parentheses x close parentheses end cell row cell g to the power of apostrophe open parentheses x close parentheses end cell equals cell 1 over open parentheses x cubed plus 2 close parentheses to the power of 5 times 15 x squared open parentheses x cubed plus 2 close parentheses to the power of 4 end cell row cell g to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 15 x squared over denominator x cubed plus 2 end fraction end cell end table end style$

Kemudian, didapat

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell ln invisible function application open parentheses x cubed plus 2 close parentheses to the power of 5 minus cos invisible function application 2 x end cell row cell f open parentheses x close parentheses end cell equals cell g open parentheses x close parentheses minus h open parentheses x close parentheses end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell g to the power of apostrophe open parentheses x close parentheses minus h to the power of apostrophe open parentheses x close parentheses end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 15 x squared over denominator x cubed plus 2 end fraction minus open parentheses negative 2 sin invisible function application 2 x close parentheses end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 15 x squared over denominator x cubed plus 2 end fraction plus 2 sin invisible function application 2 x end cell end table end style$

Jadi, jawaban yang tepat adalah A.