What is implicit 3x^3+9xy^2=5x^3 ?

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

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implicit 3x^3+9xy^2=5x^3

implicit derivative

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} (e^{\frac{( x ^{2} )}{2}})

\int (5 x - 2)^{3} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} y^{0}

\frac{d ^{2}}{d x ^{2}} (e^{3 x} cos (2 x))

\frac{d}{d x} (9 sin (x) cos (x))

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