What is derivative of e^xy=2y ?

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

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derivative of e^xy=2y

derivative of

e^{x} y = 2 y

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

Solution steps

e^{x} y = 2 y

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

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

\frac{x ^{2}}{18} + \frac{y ^{2}}{8} = 1

x^{3} + y^{3} = 3 x y

x^{3} + 3 x^{4} y = 4 y^{2} - 9

100 x y + y^{2} = 5000000

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