6. A curve \(C\) has equation
$$y = x ^ { \sin x } \quad x > 0 \quad y > 0$$
- Find, by firstly taking natural logarithms, an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
- Hence show that the \(x\) coordinates of the stationary points of \(C\) are solutions of the equation
$$\tan x + x \ln x = 0$$