- A curve \(C\) has equation
$$3 ^ { x } + x y = x + y ^ { 2 } , \quad y > 1$$
The point \(P\) with coordinates \(( 4,11 )\) lies on \(C\).
Find the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at the point \(P\).
Give your answer in the form \(a + b \ln 3\), where \(a\) and \(b\) are rational numbers.