14. The curve \(C\) has equation
$$y = \operatorname { arcsec } \mathrm { e } ^ { x } , \quad x > 0 , \quad 0 < y < \frac { 1 } { 2 } \pi$$
- Prove that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { \sqrt { \left( \mathrm { e } ^ { 2 x } - 1 \right) } }\).
- Sketch the graph of \(C\).
The point \(A\) on \(C\) has \(x\)-coordinate \(\ln 2\). The tangent to \(C\) at \(A\) intersects the \(y\)-axis at the point \(B\).
- Find the exact value of the \(y\)-coordinate of \(B\).