A curve $$\(C\)$$ has equation $$\[ y=x^{\sin x} \quad x> 0 \quad y> 0 \]$$ (a) Find, by firstly taking natural logarithms, an expression for $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ in terms of $$\(x\)$$ and $$\(y\)$$. (5) (b) Hence show that the $$\(x\)$$ coordinates of the stationary points of $$\(C\)$$ are solutions of the equation $$\[ \tan x+x \ln x=0 \]$$ (2)

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