What is derivative of y^3-3xy^2=x^3+3x^2y ?

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

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derivative of y^3-3xy^2=x^3+3x^2y

derivative of

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{x ^{2}}{18} + \frac{y ^{2}}{8} = 1

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

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

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