The curve \(C\) has equation
\[y^{2}+(x y+1)^{2}=5 .\]
(a) Show that, at the point \((1,1)\) on \(C, \frac{\mathrm{~d} y}{\mathrm{~d} x}=-\frac{2}{3}\).
(b) Find the value of \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) at the point \((1,1)\).