October 7, 2024
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 […]
