The volume \(V\) \(l\) of water flowing through a pipe is given by \(V = {t^2} + 3t\). Find the instantaneous rate of change of \(V\) when \(t = 2\) min.

The mass in grams of a melting ice-block is given by \(M = 100 + t - 2{t^2}\). Find the instantaneous rate of change of \(M\) when \(t = 2\) minutes.

The surface area of a balloon being inflated is given by \(S = {t^3} - 2{t^2} + 5t + 2\) where \(S\) is in \(\text{cm}^2\) and \(t\) is in seconds. Find the rate of increase when \(t = 4\) seconds.

Given \(f\left( t \right) = \sin 2t\), find the rate of change when \(t = \dfrac{\pi }{6}\).