Calculus: Derivatives – The Chain Rule – #148


Question: Given the parametric equations

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

(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.

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