Implicit Differentiation in multivariate calculus Let $y(x)$ be the be given explicitly by the equation : 
$xy\left( x\right) -\ln y\left( x\right) = 1$ 
Determine $\dfrac {dy}{dx}$
I'm unsure of how to go about this problem. 

Deriving with respect to $x$ we have:
$$
\frac{d}{dx}(xy)-\frac{d}{dx}(\ln y)+\frac{d}{dx}(-1)=0
$$
$$
y+x\frac{dy}{dx}-\frac{1}{y}\frac{dy}{dx}=0
$$
$$
\frac{dy}{dx}\left(x-\frac{1}{y} \right)=-y
$$
$$
\frac{dy}{dx}=\frac{y^2}{1-xy}
$$
