2.
$$f ( x ) = \tanh ^ { - 1 } \left( \frac { 3 - x } { 6 + x } \right) \quad | x | < \frac { 3 } { 2 }$$
- Show that
$$f ^ { \prime } ( x ) = - \frac { 1 } { 2 x + 3 }$$
- Hence determine \(\mathrm { f } ^ { \prime \prime } ( x )\)
- Hence show that the Maclaurin series for \(\mathrm { f } ( x )\), up to and including the term in \(x ^ { 2 }\), is
$$\ln p + q x + r x ^ { 2 }$$
where \(p , q\) and \(r\) are constants to be determined.