- A curve \(C\) has equation
$$y = 2 + 10 x ^ { \frac { 1 } { 2 } } - 2 x ^ { \frac { 3 } { 2 } } \quad x > 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) giving your answer in simplest form.
- Hence find the exact value of the gradient of the tangent to \(C\) at the point where \(x = 2\) giving your answer in simplest form.
(Solutions relying on calculator technology are not acceptable.)