What is derivative of x^2+2xy=y^2 ?

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

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derivative of x^2+2xy=y^2

derivative of

x^{2} + 2 x y = y^{2}

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

Solution steps

x^{2} + 2 x y = y^{2}

Treat

y

y (x)

Differentiate both sides:

2 x + 2 (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{x + y}{x - y}

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

d er i v a t i v e x^{3} + x^{2} y + 7 x y^{2} + y^{3} = 81

d er i v a t i v e y - 4 = 2 (x - 1)^{2}

d er i v a t i v e x y = y^{2}

d er i v a t i v e x^{3} y^{2} - 2 y = 4

d er i v a t i v e y + sin (y) = x^{2}

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