What is implicit (dy)/(dx),6x^3+7y^3=13xy ?

The answer to implicit (dy)/(dx),6x^3+7y^3=13xy is (dy)/(dx)=(13y-18x^2)/(21y^2-13x)

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implicit (dy)/(dx),6x^3+7y^3=13xy

implicit derivative

\frac{d y}{d x}, 6 x^{3} + 7 y^{3} = 13 x y

\frac{d y}{d x} = \frac{13 y - 18 x ^{2}}{21 y ^{2} - 13 x}

Solution steps

6 x^{3} + 7 y^{3} = 13 x y

Treat

y

y (x)

Differentiate both sides:

18 x^{2} + 21 y^{2} \frac{d y}{d x} = 13 (y + x \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{13 y - 18 x ^{2}}{21 y ^{2} - 13 x}

\frac{d y}{d x} = \frac{13 y - 18 x ^{2}}{21 y ^{2} - 13 x}

What is implicit (dy)/(dx),6x^3+7y^3=13xy ?
The answer to implicit (dy)/(dx),6x^3+7y^3=13xy is (dy)/(dx)=(13y-18x^2)/(21y^2-13x)