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

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

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

implicit derivative

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

\frac{d y}{d x} = \frac{1 - y}{x - 2}

Solution steps

x y = 2 y + x

Treat

y

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} = 2 \frac{d y}{d x} + 1

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1 - y}{x - 2}

\frac{d y}{d x} = \frac{1 - y}{x - 2}

f (x) = - x^{3} + x^{2} + 4 x - 2

\frac{d}{d x} (e^{- 3 x} (2 cos (2 x) - 3 sin (2 x)))

x \to 0 lim (\frac{2}{3 - e ^{\frac{1}{x}}})

\int \frac{1}{x ( 1 - x )} d x

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