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

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

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

implicit derivative

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

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

Solution steps

x y = x + y

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{d}{d x} (\frac{x + 4}{x})

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

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

\int \frac{e ^{7 x}}{e ^{7 x} + 8} d x

\int \frac{1}{( y - 1 ) ^{\frac{1}{3}}} d y

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