The derivative of $e^{nx}$ is $\boxed{n\cdot e^{nx}}$. In this article, we will be exploring why.
Recall that the Chain Rule states:

\[\begin{align*} \dfrac{d}{dx}(f(g(x))) = f'(g(x)) \cdot g'(x), \end{align*}\]

where $f(x)$ and $g(x)$ are functions. In this case, we let $f(x) = e^x$ and $g(x) = nx$ so that $f(g(x)) = e^{g(x)} = e^{nx}$.
The next step is to find the derivative of $f(x)$ and $g(x)$. For $f(x)$, we use the formula for the derivative of $e^x$, and for $g(x)$, we use the Power Rule, which states:

\[\begin{align*} \dfrac{d}{dx}(x^n)= nx^{n-1}. \end{align*}\]

Applying this to our functions, we have

\[\begin{align*} f(x) = e^x &\longrightarrow f'(x) = e^x\\ g(x) = nx &\longrightarrow g'(x) = n. \end{align*}\]

Finally, we plug these values into the Chain Rule formula and we find that:

\[\begin{align*} \dfrac{d}{dx}(e^{nx}) = e^{g(x)} \cdot n,\\ e^{g(x)} \cdot n = ne^{nx},\\ \dfrac{d}{dx}(e^{nx}) = \boxed{ne^{nx}}. \end{align*}\]