In this question, the units of \(x\) are radians and the units of \(y\) are centimetres.

It is given that \(y=(1+\cos3x)^{10}\).

(i) Find the value of \(\dfrac{dy}{dx}\) when \(x=\dfrac{\pi}{2}\).

Given also that \(y\) is increasing at a rate of \(6\text{ cm s}^{-1}\) when \(x=\dfrac{\pi}{2}\),

(ii) find the corresponding rate of change of \(x\).