JEE Math Practice Question

If xloge(logex) $$-$$ x2 + y2 = 4(y > 0), then $${{dy} \over {dx}}$$ at x = e is equal to :

1. A.$${{\left( {1 + 2e} \right)} \over {2\sqrt {4 + {e^2}} }}$$
2. B.$${{\left( {1 + 2e} \right)} \over {\sqrt {4 + {e^2}} }}$$
3. C.$${{\left( {2e - 1} \right)} \over {2\sqrt {4 + {e^2}} }}$$
4. D.$${e \over {\sqrt {4 + {e^2}} }}$$