1. The problem asks for the derivative of the function $f(x) = e^x$. 2. Recall the rule for differentiating exponential functions: the derivative of $e^x$ with respect to $x$ is $e^x$ itself. 3. This is because the exponential function $e^x$ is unique in that its rate of change is equal to its value. 4. Therefore, $$\frac{d}{dx} e^x = e^x.$$ 5. Among the options given, the correct answer is c. $e^x$.