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

The answer to implicit (dy)/(dx),3x^3y=6 is (dy}{dx}=-\frac{3y)/x

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implicit (dy)/(dx),3x^3y=6

implicit derivative

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

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

Solution steps

3 x^{3} y = 6

Treat

y

y (x)

Differentiate both sides:

3 (3 x^{2} y + \frac{d y}{d x} x^{3}) = 0

Isolate

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

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

d er i v a t i v e f (x) = - \frac{1}{4} x^{4} + \frac{27}{2} x^{2}

\int \frac{m ^{2}}{m + 1} d m

\frac{d}{d x} (\frac{x + 10}{x - 10})

\int x 1 + x d x

d er i v a t i v e ln (8 x + 5)

What is implicit (dy)/(dx),3x^3y=6 ?
The answer to implicit (dy)/(dx),3x^3y=6 is (dy}{dx}=-\frac{3y)/x