What is derivative of xy^2-x^2y-2=0 ?

The answer to derivative of xy^2-x^2y-2=0 is (dy)/(dx)=(-y^2+2xy)/(x(-x+2y))

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derivative of xy^2-x^2y-2=0

derivative of

x y^{2} - x^{2} y - 2 = 0

\frac{d y}{d x} = \frac{- y ^{2} + 2 x y}{x ( - x + 2 y )}

Solution steps

x y^{2} - x^{2} y - 2 = 0

Treat

y

y (x)

Differentiate both sides:

2 x y \frac{d y}{d x} + y^{2} - x^{2} \frac{d y}{d x} - 2 x y = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- y ^{2} + 2 x y}{x ( - x + 2 y )}

\frac{d y}{d x} = \frac{- y ^{2} + 2 x y}{x ( - x + 2 y )}

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

x^{2} - 10 x + y^{2} + 8 = 0

(a) y = e^{2} x + x

r = (t^{4} + 12) (t^{6} + 8)

\frac{x ^{m}}{a ^{m}} + \frac{y ^{m}}{b ^{m}} = 1

What is derivative of xy^2-x^2y-2=0 ?
The answer to derivative of xy^2-x^2y-2=0 is (dy)/(dx)=(-y^2+2xy)/(x(-x+2y))