What is derivative of x^3+y^3=3xy ?

The answer to derivative of x^3+y^3=3xy is (dy)/(dx)=(y-x^2)/(y^2-x)

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derivative of x^3+y^3=3xy

derivative of

x^{3} + y^{3} = 3 x y

\frac{d y}{d x} = \frac{y - x ^{2}}{y ^{2} - x}

Solution steps

x^{3} + y^{3} = 3 x y

Treat

y

y (x)

Differentiate both sides:

3 x^{2} + 3 y^{2} \frac{d y}{d x} = 3 (y + x \frac{d y}{d x})

Isolate

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

\frac{d y}{d x} = \frac{y - x ^{2}}{y ^{2} - x}

x^{3} + 3 x^{4} y = 4 y^{2} - 9

100 x y + y^{2} = 5000000

\frac{sin ( x y ) + x}{y} = x^{2} - y

ln (x^{6} + y^{20}) = sin (x) + e^{y}

x y^{2} - x^{2} y - 2 = 0

What is derivative of x^3+y^3=3xy ?
The answer to derivative of x^3+y^3=3xy is (dy)/(dx)=(y-x^2)/(y^2-x)