Question: Given the parametric equations

\[\left\{ \begin{aligned} & x=2t+\frac{1}{t},\,\,\,t>0 \\ & y=t+1 \\ \end{aligned} \right.\]

(a) Find \(\frac{dy}{dx}\) and the slope of the tangent at t = 1.

(b) Find \(\frac{{{d}^{2}}y}{d{{x}^{2}}}\) and the slope of the tangent at t = 1.