Derivative of 2/e^x

1. The derivative of a constant times a function is the constant times the derivative of the function.

   1. Let $u = e^{x}$.

   2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} e^{x}$:

      1. The derivative of $e^{x}$ is itself.

      The result of the chain rule is:

      $$- e^{- x}$$

   So, the result is: $- 2 e^{- x}$

The answer is:

$$- 2 e^{- x}$$