2025 IGCSE Additional Mathematics October/November 0606/12 Q12

A curve has equation \(y=\dfrac{\mathrm e^{x^2}}{x-2}\) for \(x<2\).

1. Find the value of \(\dfrac{\mathrm dy}{\mathrm dx}\) when \(x=0\).[4]
   When \(x=0\), \(y\) is increasing at the rate of 0.5 units per second.
2. Find the corresponding rate of change of \(x\).[2]