How can we differentiate the Riemann-Liouville fractional differintegral $\Large\mathrm{D}_x^{-s}\LARGE(\Large{\frac{e^{2\pi ix}}{1-e^{2\pi ix}}}\LARGE)$ by minus the order to which it is fractionally differintegrated, namely $s$, taking the base point of the fractional differintegral to be $-\infty$? In other words, what is
$\frac{d}{ds}\LARGE[\small{_-\infty}\Large\mathrm{D}_x^{-s}\LARGE(\Large{\frac{e^{2\pi ix}}{1-e^{2\pi ix}}}\LARGE)\LARGE]$
?