What is derivative of xy=y^2 ?

The answer to derivative of xy=y^2 is (dy)/(dx)=-y/(x-2y)

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derivative of xy=y^2

derivative of

x y = y^{2}

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

Solution steps

x y = y^{2}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

x^{3} y^{2} - 2 y = 4

y + sin (y) = x^{2}

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

x = tan^{2} (y)

y^{2} = 40 x

What is derivative of xy=y^2 ?
The answer to derivative of xy=y^2 is (dy)/(dx)=-y/(x-2y)