Pertanyaan

Jika diketahui kurva x 3 y 2 − y 3 = 2 , maka d x d y = .....

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

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

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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, dan Oleh karena itu, Jadi, jawaban yang tepat adalah B.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x cubed y squared minus y cubed end cell equals 2 row cell fraction numerator d over denominator d x end fraction open parentheses x cubed y squared minus y cubed close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 2 close parentheses end cell row cell fraction numerator d over denominator d x end fraction open parentheses x cubed y squared close parentheses minus fraction numerator d over denominator d x end fraction open parentheses y cubed close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 2 close parentheses end cell end table end style$

Selanjutnya, perhatikan bahwa

$begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses 2 close parentheses equals 0 end style$

Kemudian,

dan

$begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses y cubed close parentheses equals 3 y squared times fraction numerator d y over denominator d x end fraction end style$

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 cubed y squared close parentheses minus fraction numerator d over denominator d x end fraction open parentheses y cubed close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 2 close parentheses end cell row cell open parentheses 3 x squared y squared plus 2 x cubed y times fraction numerator d y over denominator d x end fraction close parentheses minus 3 y squared times fraction numerator d y over denominator d x end fraction end cell equals 0 row cell 3 x squared y squared plus 2 x cubed y times fraction numerator d y over denominator d x end fraction minus 3 y squared times fraction numerator d y over denominator d x end fraction end cell equals 0 row cell 3 x squared y squared plus open parentheses 2 x cubed y minus 3 y squared close parentheses fraction numerator d y over denominator d x end fraction end cell equals 0 row cell open parentheses 2 x cubed y minus 3 y squared close parentheses fraction numerator d y over denominator d x end fraction end cell equals cell negative 3 x squared y squared end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell negative fraction numerator 3 x squared y squared over denominator 2 x cubed y minus 3 y squared end fraction end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell fraction numerator 3 x squared y squared over denominator negative open parentheses 2 x cubed y minus 3 y squared close parentheses end fraction end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell fraction numerator 3 x squared y squared over denominator 3 y squared minus 2 x cubed y end fraction end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell fraction numerator 3 x squared y squared over denominator y open parentheses 3 y minus 2 x cubed close parentheses end fraction end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell fraction numerator 3 x squared y over denominator 3 y minus 2 x cubed end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah B.