6 You are given that \(y = \tan ^ { - 1 } \sqrt { 2 x }\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Show that \(\int _ { \frac { 1 } { 6 } } ^ { \frac { 1 } { 2 } } \frac { \sqrt { x } } { \left( x + 2 x ^ { 2 } \right) } \mathrm { d } x = k \pi\) where \(k\) is a number to be determined in exact form.