1. **State the problem:** Find the derivative of the function $f(x) = e^x$. 2. **Formula used:** The derivative of the exponential function $e^x$ with respect to $x$ is given by: $$\frac{d}{dx} e^x = e^x$$ This is a fundamental rule in calculus because the function $e^x$ is unique in that its rate of change is equal to its value. 3. **Intermediate work:** Since the derivative of $e^x$ is $e^x$, no further simplification is needed. 4. **Explanation:** The function $e^x$ grows at a rate proportional to its current value, which means the slope of the tangent line at any point $x$ on the curve is exactly $e^x$. **Final answer:** $$\frac{d}{dx} e^x = e^x$$