Find $\frac{d s}{d t}$ \[ s=2 \cot t-e^{-t} \]

Step 1 ：Given the function \(s=2 \cot t-e^{-t}\).

Step 2 ：We are asked to find the derivative of this function with respect to \(t\).

Step 3 ：Using the rules of differentiation, the derivative of \(\cot t\) is \(-\csc^2 t\) and the derivative of \(e^{-t}\) is \(-e^{-t}\).

Step 4 ：Applying these rules to our function, we find that the derivative of \(s=2 \cot t-e^{-t}\) with respect to \(t\) is \(-2 \csc^2 t + e^{-t}\).

Step 5 ：Final Answer: \(\boxed{-2 \csc^2 t + e^{-t}}\)