Let $y=y(x)$ be a function implicitly defined as $$xy+\ln(xy)=1$$ near a point $P(1,1)$. 

I have to find the explicit expression $y(x)$ as well as the values $y'(1)$ and $dy(1)$.

I've tried applying the exponential to both sides but I could not find a solution: $$ e^{xy}xy=e $$ doesn't seem to be very helpful.

Also, using implicit differentiation didn't help me that much with obtaining $y'(1)$. If I am not mistaking, by implicit differentiation one obtains 
$$y+xy'+\frac{1}{x}+\frac{y'}{y}=0$$

But I still can't see how I can obtain the value $y'(1)$ from this. As for $dy(1)$: I have no idea how I could obtain that!

Any help/suggestions would be appreciated.