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

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{-2 \csc^2 t + e^{-t}}$

Steps

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: $\boxed{-2 \csc^2 t + e^{-t}}$