(a) Differentiate \(x\ln x-2x\) with respect to \(x\), simplifying your answer.

(b) A curve is such that

\(\displaystyle \frac{d^2y}{dx^2}=\left(\frac{x+1}{\sqrt{x}}\right)^2\).

At the point \(\left(\mathrm{e},\frac{\mathrm{e}^3}{6}+\mathrm{e}^2\right)\), the gradient of the curve is \(\frac{\mathrm{e}^2}{2}+2\mathrm{e}\). Using your answer to part (a), find the exact equation of the curve.