2 It is given that \(y = 2 ^ { x }\).
- By differentiating \(\ln y\) with respect to \(x\), show that \(\frac { \mathrm { dy } } { \mathrm { dx } } = 2 ^ { \mathrm { x } } \ln 2\).
- Write down \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\).
- Hence find the first three terms in the Maclaurin's series for \(2 ^ { X }\).