The curve \(C\) has equation
\(9 y^{2}-3 \sinh ^{-1}(x y)=1-3 \ln 3 .\)
(a) Show that, at the point \(\left(4, \frac{1}{3}\right)\) on \(C, \frac{\mathrm{~d} y}{\mathrm{~d} x}=-\frac{1}{2}\).
(b) Find the value of \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) at the point \(\left(4, \frac{1}{3}\right)\).