A curve \(C\) has equation \(xy=\ln y\), where \(y>0\).
Find \(\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}\) in terms of \(x\) and \(y\), and hence show that \(C\) has no stationary points.[3]
Find the equation of the tangent to \(C\) at the point where \(y=e^2\). Give your answer in the form \(y=mx+c\), where \(m\) and \(c\) are exact values.[3]