Pertanyaan

Jika diketahui kurva x y 2 + x 2 y + 5 = x 3 + y 4 , maka d x d y = ...

Jika diketahui kurva $x y^{2} + x^{2} y + 5 = x^{3} + y^{4}$ , maka $\frac{d y}{d x} =$ ...

$begin mathsize 14px style fraction numerator 3 x squared plus y squared plus 2 x y over denominator 2 x y plus x squared minus 4 y cubed end fraction end style$
$begin mathsize 14px style fraction numerator 3 x squared minus y squared minus 2 x y over denominator 2 x y plus x squared minus 4 y cubed end fraction end style$
$begin mathsize 14px style fraction numerator 3 x squared plus y squared plus 2 x y over denominator 2 x y minus x squared plus 4 y cubed end fraction end style$
$begin mathsize 14px style fraction numerator 3 x squared minus y squared minus 2 x y over denominator 2 x y minus x squared plus 4 y cubed end fraction end style$
$begin mathsize 14px style fraction numerator 3 x squared plus y squared minus 2 x y over denominator 2 x y plus x squared plus 4 y cubed end fraction end style$

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 B.

Pembahasan

Perhatikan bahwa Selanjutnya, perhatikan bahwa Kemudian, didapat bahwa Selanjutnya, dan Oleh karena itu, Jadi, jawaban yang tepat adalah B.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x y squared plus x squared y plus 5 end cell equals cell x cubed plus y to the power of 4 end cell row cell fraction numerator d over denominator d x end fraction open parentheses x y squared plus x squared y plus 5 close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses x cubed plus y to the power of 4 close parentheses end cell row cell fraction numerator d over denominator d x end fraction open parentheses x y squared close parentheses plus fraction numerator d over denominator d x end fraction open parentheses x squared y close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 5 close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses x cubed close parentheses plus fraction numerator d over denominator d x end fraction open parentheses y to the power of 4 close parentheses end cell end table end style$

Selanjutnya, perhatikan bahwa

Kemudian, didapat bahwa

Selanjutnya,

dan

$begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses y to the power of 4 close parentheses equals 4 y cubed times fraction numerator d y over denominator d x end fraction end style$

Oleh karena itu,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses x y squared close parentheses plus fraction numerator d over denominator d x end fraction open parentheses x squared y close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 5 close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses x cubed close parentheses plus fraction numerator d over denominator d x end fraction open parentheses y to the power of 4 close parentheses end cell row cell open parentheses y squared plus 2 x y times fraction numerator d y over denominator d x end fraction close parentheses plus open parentheses 2 x y plus x squared times fraction numerator d y over denominator d x end fraction close parentheses plus 0 end cell equals cell 3 x squared plus 4 y cubed times fraction numerator d y over denominator d x end fraction end cell row cell y squared plus 2 x y times fraction numerator d y over denominator d x end fraction plus 2 x y plus x squared times fraction numerator d y over denominator d x end fraction end cell equals cell 3 x squared plus 4 y cubed times fraction numerator d y over denominator d x end fraction end cell row cell 2 x y times fraction numerator d y over denominator d x end fraction plus x squared times fraction numerator d y over denominator d x end fraction minus 4 y cubed times fraction numerator d y over denominator d x end fraction end cell equals cell 3 x squared minus y squared minus 2 x y end cell row cell open parentheses 2 x y plus x squared minus 4 y cubed close parentheses times fraction numerator d y over denominator d x end fraction end cell equals cell 3 x squared minus y squared minus 2 x y end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell fraction numerator 3 x squared minus y squared minus 2 x y over denominator 2 x y plus x squared minus 4 y cubed end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah B.