- (a) Prove, by using logarithms, that
$$\frac { \mathrm { d } } { \mathrm {~d} x } \left( 2 ^ { x } \right) = 2 ^ { x } \ln 2$$
The curve \(C\) has the equation
$$2 x + 3 y ^ { 2 } + 3 x ^ { 2 } y + 12 = 4 \times 2 ^ { x }$$
The point \(P\), with coordinates \(( 2,0 )\), lies on \(C\).
(b) Find an equation of the tangent to \(C\) at \(P\).