What is implicit (dy)/(dx),e^{x/y}=x-y ?

The answer to implicit (dy)/(dx),e^{x/y}=x-y is (dy)/(dx)=(y^2-e^{x/y}y)/(-e^{x/y)x+y^2}

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implicit (dy)/(dx),e^{x/y}=x-y

implicit derivative

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

\frac{e ^{\frac{x}{y}} ( y - x \frac{d y}{d x} )}{y ^{2}} = 1 - \frac{d y}{d x}

Isolate

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

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

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