2 The curve \(C\) has equation
$$4 y ^ { 2 } + 4 \ln ( x y ) = 1 .$$
- Show that, at the point \(\left( 2 , \frac { 1 } { 2 } \right)\) on \(C , \frac { \mathrm {~d} y } { \mathrm {~d} x } = - \frac { 1 } { 6 }\).
\includegraphics[max width=\textwidth, alt={}, center]{bc601b16-c106-43a2-a2fc-676b5c836096-04_2718_35_107_2012}
\includegraphics[max width=\textwidth, alt={}, center]{bc601b16-c106-43a2-a2fc-676b5c836096-05_2725_35_99_20} - Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the point \(\left( 2 , \frac { 1 } { 2 } \right)\).