Why the differentiation of $e^x$ is $e^x?$ $$\frac{d}{dx} e^x=e^x$$
Please explain simply as I haven't studied the first principle of differentiation yet, but I know the basics of differentiation.

The number $e$ is defined by: $e=\sum\limits_{n=0}^\infty\dfrac{1}{n!}$ but historically I think that the definition of the $exp$ function is: $e^x=\lim\limits_{n\to+\infty}\left(1+\dfrac{x}{n}\right)^n$ and the properties of this function comes from this definition as shown in this article.
