Given that \(y = \ln ( 4 + 3 x )\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
Hence, by using Maclaurin's theorem, find the first three terms in the expansion, in ascending powers of \(x\), of \(\ln ( 4 + 3 x )\).
Write down the first three terms in the expansion, in ascending powers of \(x\), of \(\ln ( 4 - 3 x )\).
Show that, for small values of \(x\),
$$\ln \left( \frac { 4 + 3 x } { 4 - 3 x } \right) \approx \frac { 3 } { 2 } x$$