This article will teach you how to take the derivative of $4e^x$, as well as the proof for why the derivative is correct.
Taking the Derivative
Let us take the derivative of $\ln e^x$. Of course, $\ln e^x = x$, so the derivative should equal $1$. Using the chain rule, we get that $\frac{d}{dx} \ln e^x = \frac{1}{e^x} * \frac{d}{dx} e^x = 1 \to \frac{d}{dx} e^x = e^x$. Therefore, $\frac{d}{dx} ke^x$, where $k$ is a constant, is simply $ke^x$!
Conclusion
This example shows us that sometimes we need to use special tricks to find the derivative of a function. It is much harder to take the derivative of $e^x$ using the definition of a derivative than to simply take the derivative of $\ln e^x$. Additionally, you now know the derivative of $e^x$ and the reasoning behind it! Good luck on your future math adventures!
