What is implicit (dy)/(dx),x+y=xy ?

The answer to implicit (dy)/(dx),x+y=xy is (dy)/(dx)=(y-1)/(1-x)

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implicit (dy)/(dx),x+y=xy

implicit derivative

\frac{d y}{d x}, x + y = x y

\frac{d y}{d x} = \frac{y - 1}{1 - x}

Solution steps

x + y = x y

Treat

y

y (x)

Differentiate both sides:

1 + \frac{d y}{d x} = y + x \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{y - 1}{1 - x}

\frac{d y}{d x} = \frac{y - 1}{1 - x}

\frac{d y}{d x} = \frac{x ^{3} + 4 y ^{3}}{3 x y ^{2}}

\frac{d}{d x} (2 x^{2} - \frac{1}{x})

\int_{0}^{8} 1

x \to 3 lim (x^{2} - 4 x + 10)

\int tan^{3} (5 x) sec (5 x) d x

What is implicit (dy)/(dx),x+y=xy ?
The answer to implicit (dy)/(dx),x+y=xy is (dy)/(dx)=(y-1)/(1-x)