What is implicit x^3y^3-y=x ?

The answer to implicit x^3y^3-y=x is (dy)/(dx)=(1-3x^2y^3)/(3x^3y^2-1)

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implicit x^3y^3-y=x

implicit derivative

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

\frac{d y}{d x} = \frac{1 - 3 x ^{2} y ^{3}}{3 x ^{3} y ^{2} - 1}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

3 x^{2} y^{3} + 3 y^{2} \frac{d y}{d x} x^{3} - \frac{d y}{d x} = 1

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1 - 3 x ^{2} y ^{3}}{3 x ^{3} y ^{2} - 1}

\frac{d y}{d x} = \frac{1 - 3 x ^{2} y ^{3}}{3 x ^{3} y ^{2} - 1}

\frac{d}{d x} (sin (x) + cos (y))

f (x) = \frac{3}{2 x - 4}

\frac{\partial}{\partial x} (x e^{4 y} sin (3 z))

\int \frac{2}{x ^{2} + 10 x + 29} d x

(1 + x^{2}) \frac{d y}{d x} - (1 + y^{2}) = 0

What is implicit x^3y^3-y=x ?
The answer to implicit x^3y^3-y=x is (dy)/(dx)=(1-3x^2y^3)/(3x^3y^2-1)