To find the derivative of the function $f(x) = a^x$, where $a$ is a constant, we can use the following formula:

$\frac{d}{dx} a^x = a^x \ln(a)$

So, the derivative of $a^x$ is:

$f'(x) = a^x \ln(a)$

If you need further details or have any questions, feel free to ask! Here are some related questions to consider:

1. What is the derivative of $e^x$?
2. How do you differentiate $a^{kx}$ where $k$ is a constant?
3. Can you explain the significance of the natural logarithm in this context?
4. How would you apply this derivative in real-world scenarios?
5. What are some properties of exponential functions?

Tip: Remember that the base $a$ must be positive and not equal to 1 for the function $a^x$ to be valid.