1 A curve \(C\) has equation \(\cos y = x\), for \(- \pi < x < \pi\).
- Use implicit differentiation to show that
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = - \cot y \left( \frac { \mathrm {~d} y } { \mathrm {~d} x } \right) ^ { 2 }$$
- Hence find the exact value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the point \(\left( \frac { 1 } { 2 } , \frac { 1 } { 3 } \pi \right)\) on \(C\).