Introduction
Hello everyone! In this article, we will review how to take the derivative of $4^x$. This is a very instructive example for how to take the derivative of an exponential function with a base other than $e$, which is a very important concept to understand. Without further ado, let’s get into it!
Taking the Derivative
We first express $4^x$ as an exponential function with base $e$: $4^x = (e^{\ln4})^x = e^{x\ln4}.$ Now, we can use the Chain Rule to find that the derivative is $\ln4 * e^{x\ln4}$, which we can rewrite as $\ln4 * 4^x$. Therefore, the derivative of $n^x$ (where $n$ is constant) is $\ln n * n^x$.
Conclusion
You now should know how to take the derivative of $4^x$ and every other exponential function with a base other than $e$. I hope this article helped you, and good luck on your future math adventures!