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

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

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

implicit derivative

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{3 x ^{2} + 8 x + 2}{x ( x + 1 ) ^{2}}

\frac{x ^{2} + 6 x + 1}{( x + 3 ) ^{2}}

(6 x - 2 y) (3 - y^{'} (x))

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

\frac{x - 5}{( x - 9 ) ( x + 8 )}

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