If $x^y = e^{x-y}$, then $\frac{dy}{dx}$ is :

Question

( A ) $\frac{1+x}{1 + \log x}$
( B ) $\frac{1 - \log x}{1+ \log x}$
( C ) $\frac{\log x}{(1+ \log x)^2}$
( D ) not defined