# If $e^{x+y}=xy,$ what is $\large\frac{dy}{dx}$?
$\begin{array}{1 1}(A)\;\large\frac{y(1-x)}{x(y-1)}\\(B)\;\large\frac{y(1+x)}{x(y-1)}\\(C)\;\large\frac{y(1-x)}{x(1+y)}\\(D)\;\large\frac{y(1+x)}{x(1-y)}\end{array}$