Differentiate `e^(-x)` from first principles

Explanation

To differentiate \( e^{-x} \) from first principles, we follow these steps:

### Step 1: Define the function
Let \( f(x) = e^{-x} \).

### Step 2: Use the definition of the derivative
According to the first principles of differentiation, the derivative \( f'(x) \) is given by:
\[
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