It is given that

\(y=(1+e^{x^2})(x+5).\)

(i) Find \(\frac{dy}{dx}\).

(ii) Find the approximate change in \(y\) as \(x\) increases from \(0.5\) to \(0.5+p\), where \(p\) is small.

(iii) Given that \(y\) is increasing at a rate of \(2\) units per second when \(x=0.5\), find the corresponding rate of change in \(x\).