# What's in the denominator?

Calculus Level 3

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

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

where $$f(x)$$ is a function involving $$x$$ (not necessarily equalling $$y$$), find $$f(x)$$.

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