We will be finding the derivative of $a^x$ where $a$ is a constant. We will start by rewriting $a^x$ as:
\[\begin{align*} a^x = (e^{\ln a})^x = e^{\ln a \cdot x}. \end{align*}\]
Now, recall the formula $\dfrac{d}{dx}(e^{nx}) = e^{nx} \cdot n$. In the context of our problem, $n = \ln a$. More information on this formula can be found here: (insert link to $e^{nx}$ equation).
Applying this to our expression, we get:
\[\begin{align*} \dfrac{d}{dx}(e^{\ln a \cdot x}) = e^{\ln a \cdot x} \cdot \ln a = \boxed{a^x \cdot \ln a}. \end{align*}\]
In general, converting exponential functions into a form with $e$ as the base can be a helpful trick for differentiating.
