What is implicit (dy)/(dx),3x^3+9xy^2=5x^3 ?

The answer to implicit (dy)/(dx),3x^3+9xy^2=5x^3 is (dy)/(dx)=(2x^2-3y^2)/(6xy)

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implicit (dy)/(dx),3x^3+9xy^2=5x^3

implicit derivative

\frac{d y}{d x}, 3 x^{3} + 9 x y^{2} = 5 x^{3}

\frac{d y}{d x} = \frac{2 x ^{2} - 3 y ^{2}}{6 x y}

Solution steps

3 x^{3} + 9 x y^{2} = 5 x^{3}

Treat

y

y (x)

Differentiate both sides:

9 x^{2} + 9 (y^{2} + 2 x y \frac{d y}{d x}) = 15 x^{2}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{2 x ^{2} - 3 y ^{2}}{6 x y}

\frac{d y}{d x} = \frac{2 x ^{2} - 3 y ^{2}}{6 x y}

\frac{d}{d x} (\frac{x ^{2} + 3 x + 2}{x + 1})

\frac{9}{( s - 2 ) ( s - 3 )}

f (x) = (2 x) (4 x^{2} + 6 x^{7} + 8)

\int \frac{1}{b ^{2} + a ^{2} x ^{2}} d x

\int x^{2} ln (x) + e^{2 x} + 1 d x

What is implicit (dy)/(dx),3x^3+9xy^2=5x^3 ?
The answer to implicit (dy)/(dx),3x^3+9xy^2=5x^3 is (dy)/(dx)=(2x^2-3y^2)/(6xy)