Differentiate the following w.r.t. $x : sin\;( tan^{-1} e^{-x}) $

Question

$\begin{array}{1 1} - \large\frac{cos(tan^{-1}e^{-x})e^{-x}}{1+e^{-2x}} \\ - \large\frac{sin(tan^{-1}e^{-x})e^{-x}}{1+e^{-2x}} \\ - \large\frac{cos(tan^{-1}e^{-x})e^{-x}}{1-2e^{-2x}} \\ - \large\frac{sin(tan^{-1}e^{-x})e^{-x}}{1-2e^{-2x}} \end{array} $