- Given that
$$x = \sec ^ { 2 } 3 y , \quad 0 < y < \frac { \pi } { 6 }$$
- find \(\frac { \mathrm { d } x } { \mathrm {~d} y }\) in terms of \(y\).
- Hence show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 6 x ( x - 1 ) ^ { \frac { 1 } { 2 } } }$$
- Find an expression for \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) in terms of \(x\). Give your answer in its simplest form.