4 The equation of a curve is \(y = \frac { x ^ { 2 } } { 2 x + 1 }\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x ( x + 1 ) } { ( 2 x + 1 ) ^ { 2 } }\).
- Find the coordinates of the stationary points of the curve. You need not determine their nature.
- Differentiate \(\sqrt { 1 + 2 x }\).
- Show that the derivative of \(\ln \left( 1 - \mathrm { e } ^ { - x } \right)\) is \(\frac { 1 } { \mathrm { e } ^ { x } - 1 }\).