The curve \(C\) has equation
\(4 y^{2}+4 \ln (x y)=1 .\)
(a) Show that, at the point \(\left(2, \frac{1}{2}\right)\) on \(C, \frac{\mathrm{~d} y}{\mathrm{~d} x}=-\frac{1}{6}\).
(b) Find the value of \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) at the point \(\left(2, \frac{1}{2}\right)\).