It is given that \(y=2^{x}\).
(a) By differentiating \(\ln y\) with respect to \(x\), show that \(\frac{\mathrm{d} y}{\mathrm{~d} x}=2^{x} \ln 2\).
(b) Write down \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\).

(c) Hence find the first three terms in the Maclaurin's series for \(2^{x}\).