What is implicit (dy)/(dx),2xy-4y=xy-xy^2 ?

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

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implicit (dy)/(dx),2xy-4y=xy-xy^2

implicit derivative

\frac{d y}{d x}, 2 x y - 4 y = x y - x y^{2}

\frac{d y}{d x} = \frac{- y ^{2} - y}{x + 2 x y - 4}

Solution steps

2 x y - 4 y = x y - x y^{2}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- y ^{2} - y}{x + 2 x y - 4}

\frac{d y}{d x} = \frac{- y ^{2} - y}{x + 2 x y - 4}

y^{^{'}} = \frac{9 x ^{2} - 6}{x ^{2}}

5 x - x^{2}, x, 0, 4

n = 3 \sum \infty \frac{5 ^{n}}{1 4 ^{n}}

\int x \cdot e^{4 x} d x

x = 4 y^{3}, x = 22 y^{2}

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