What is implicit (dy)/(dx),x^3-3x^2y+2xy^2=12 ?

The answer to implicit (dy)/(dx),x^3-3x^2y+2xy^2=12 is (dy)/(dx)=(-3x^2+6xy-2y^2)/(x(-3x+4y))

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implicit (dy)/(dx),x^3-3x^2y+2xy^2=12

implicit derivative

\frac{d y}{d x}, x^{3} - 3 x^{2} y + 2 x y^{2} = 12

\frac{d y}{d x} = \frac{- 3 x ^{2} + 6 x y - 2 y ^{2}}{x ( - 3 x + 4 y )}

Solution steps

x^{3} - 3 x^{2} y + 2 x y^{2} = 12

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 3 x ^{2} + 6 x y - 2 y ^{2}}{x ( - 3 x + 4 y )}

\frac{d y}{d x} = \frac{- 3 x ^{2} + 6 x y - 2 y ^{2}}{x ( - 3 x + 4 y )}

What is implicit (dy)/(dx),x^3-3x^2y+2xy^2=12 ?
The answer to implicit (dy)/(dx),x^3-3x^2y+2xy^2=12 is (dy)/(dx)=(-3x^2+6xy-2y^2)/(x(-3x+4y))