6. (a) Given that \(y = 2 ^ { x }\), and using the result \(2 ^ { x } = \mathrm { e } ^ { x \ln 2 }\), or otherwise, show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 ^ { x } \ln 2\).
(b) Find the gradient of the curve with equation \(y = 2 ^ { \left( x ^ { 2 } \right) }\) at the point with coordinates \(( 2,16 )\).