(i) Given that \(y=x\sqrt{x^2+1}\), show that \(\dfrac{dy}{dx}=\dfrac{ax^2+b}{(x^2+1)^p}\), where \(a\), \(b\) and \(p\) are positive constants.

(ii) Explain why the graph of \(y=x\sqrt{x^2+1}\) has no stationary points.

\(y=x^3\ln(2x+1).\)

(i) Find the value of \(\dfrac{dy}{dx}\) when \(x=0.3\). You must show all your working.

(ii) Hence find the approximate increase in \(y\) when \(x\) increases from \(0.3\) to \(0.3+h\), where \(h\) is small.