Mathematics

Problem

For the implicitly defined curve

e^{xy}=x+y

, determine

\dfrac{dy}{dx}

in terms of

x

and

y

. a)

\displaystyle\frac{1-e^{xy}y}{1-e^{xy}x}

\displaystyle\frac{1-e^{xy}y}{e^{xy}x-1}

\displaystyle\frac{e^{xy}(1-y)}{e^{xy}x-1}

\displaystyle\frac{1-y}{x-1}