7 A curve has equation \(y ^ { 3 } + 2 \mathrm { e } ^ { - 3 x } y - x = k\), where \(k\) is a constant.
The point \(P \left( \ln 2 , \frac { 1 } { 2 } \right)\) lies on this curve.
- Show that the exact value of \(k\) is \(q - \ln 2\), where \(q\) is a rational number.
- Find the gradient of the curve at \(P\).