Differentiation

Let \(\mathrm{f}(x)=\log (\sin x), 0 < x < \pi\) and \(\mathrm{g}(x)=\sin ^{-1}\left(\mathrm{e}^{-x}\right), x \geq 0\). If \(\alpha\) is a positive real number such that \(\mathrm{a}=(\mathrm{fog})^{\prime}(\alpha)\) and \(\mathrm{b}=(\mathrm{fog})(\alpha)\), then