Pertanyaan

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

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

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

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Klaim

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa Selanjutnya, perhatikan bahwa Kemudian, dengan aturan perkalian pada turunan, didapat bahwa Oleh karena itu, Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa

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

Selanjutnya, perhatikan bahwa

Kemudian, dengan aturan perkalian pada turunan, didapat bahwa

Oleh karena itu,

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

Jadi, jawaban yang tepat adalah D.