8 The function f is defined by \(\mathrm { f } ( x ) = \frac { 1 } { x + 1 } + \frac { 1 } { ( x + 1 ) ^ { 2 } }\) for \(x > - 1\).
- Find \(\mathrm { f } ^ { \prime } ( x )\).
- State, with a reason, whether f is an increasing function, a decreasing function or neither.
The function g is defined by \(\mathrm { g } ( x ) = \frac { 1 } { x + 1 } + \frac { 1 } { ( x + 1 ) ^ { 2 } }\) for \(x < - 1\).
- Find the coordinates of the stationary point on the curve \(y = \mathrm { g } ( x )\).