(a) Given that \(y=\dfrac{e^{3x}}{4x^2+1}\), find \(\dfrac{dy}{dx}\).

(b) Variables \(x\), \(y\), and \(t\) are such that

\(y=4\cos\left(x+\frac{\pi}{3}\right)+2\sqrt3\sin\left(x+\frac{\pi}{3}\right)\)

and \(\dfrac{dy}{dt}=10\).

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

(ii) Find \(\dfrac{dx}{dt}\) when \(x=\dfrac{\pi}{2}\).