The equation of a curve is \(y = 4\sqrt{x} + \frac{2}{\sqrt{x}}\).

(i) Obtain an expression for \(\frac{dy}{dx}\).

(ii) A point is moving along the curve in such a way that the \(x\)-coordinate is increasing at a constant rate of 0.12 units per second. Find the rate of change of the \(y\)-coordinate when \(x = 4\).