What's in the denominator?

Calculus Level 3

Given that for x>0x>0, y=y(x)>0y=y(x)>0, ecot(y)=xx+xln(x)e^{-\cot(y)}=x^x+x\ln(x)

and implicit differentiation of the above equation gives dydx=(xx+1)(ln(x)+1)(csc2(y))(xx+xf(x))\frac{dy}{dx}=\frac{(x^x+1)(\ln(x)+1)}{(\csc^2(y))(x^x+xf(x))}

where f(x)f(x) is a function involving xx (not necessarily equalling yy), find f(x)f(x).

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