Pertanyaan

Jika diketahui kurva y 6 + x 4 = 0 , maka d x d y = ......

Jika diketahui kurva $y^{6} + x^{4} = 0$ , maka $\frac{d y}{d x} =$ ......

$begin mathsize 14px style negative fraction numerator 2 x cubed over denominator 3 y to the power of 5 end fraction end style$
$begin mathsize 14px style fraction numerator 2 x cubed over denominator 3 y to the power of 5 end fraction end style$
$begin mathsize 14px style negative fraction numerator 3 y to the power of 5 over denominator 2 x cubed end fraction end style$
$begin mathsize 14px style fraction numerator 3 y to the power of 5 over denominator 2 x cubed end fraction end style$
$begin mathsize 14px style negative fraction numerator 2 x to the power of 5 over denominator 3 y cubed end fraction end style$

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa Selanjutnya, perhatikan bahwa Kemudian, dengan aturan rantai, didapat bahwa Oleh karena itu, Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y to the power of 6 plus x to the power of 4 end cell equals 0 row cell fraction numerator d over denominator d x end fraction open parentheses y to the power of 6 plus x to the power of 4 close parentheses end cell equals 0 row cell fraction numerator d over denominator d x end fraction open parentheses y to the power of 6 close parentheses plus fraction numerator d over denominator d x end fraction open parentheses x to the power of 4 close parentheses end cell equals 0 end table end style$

Selanjutnya, perhatikan bahwa

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

Kemudian, dengan aturan rantai, didapat bahwa

$begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses y to the power of 6 close parentheses equals 6 y to the power of 5 times fraction numerator d y over denominator d x end fraction end style$

Oleh karena itu,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses y to the power of 6 close parentheses plus fraction numerator d over denominator d x end fraction open parentheses x to the power of 4 close parentheses end cell equals 0 row cell 6 y to the power of 5 times fraction numerator d y over denominator d x end fraction plus 4 x cubed end cell equals 0 row cell 6 y to the power of 5 times fraction numerator d y over denominator d x end fraction end cell equals cell negative 4 x cubed end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell negative fraction numerator 4 x cubed over denominator 6 y to the power of 5 end fraction end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell negative fraction numerator 2 x cubed over denominator 3 y to the power of 5 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah A.