What is implicit (dy)/(dx),xy=y^3 ?

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

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implicit (dy)/(dx),xy=y^3

implicit derivative

\frac{d y}{d x}, x y = y^{3}

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

Solution steps

x y = y^{3}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\int \frac{2 v}{2 - 3 v ^{2}} d v

x y^{2} - 5 y + 6

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

\int x e^{4 x} d x

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

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