Given \(y = 2 x \left( x ^ { 2 } - 1 \right) ^ { 5 }\), show that
\(\frac { \mathrm { d } y } { \mathrm {~d} x } = \mathrm { g } ( x ) \left( x ^ { 2 } - 1 \right) ^ { 4 }\) where \(\mathrm { g } ( x )\) is a function to be determined.
Hence find the set of values of \(x\) for which \(\frac { \mathrm { d } y } { \mathrm {~d} x } \geqslant 0\)
(ii) Given
$$x = \ln ( \sec 2 y ) , \quad 0 < y < \frac { \pi } { 4 }$$
find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) as a function of \(x\) in its simplest form.