What is implicit (dy)/(dx),xy+x=2 ?

The answer to implicit (dy)/(dx),xy+x=2 is (dy}{dx}=\frac{-y-1)/x

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implicit (dy)/(dx),xy+x=2

implicit derivative

\frac{d y}{d x}, x y + x = 2

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

Solution steps

x y + x = 2

Treat

y

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} + 1 = 0

Isolate

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

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

What is implicit (dy)/(dx),xy+x=2 ?
The answer to implicit (dy)/(dx),xy+x=2 is (dy}{dx}=\frac{-y-1)/x