How to derive $e^x = \lim_{n \to \infty} \left( 1 + \frac x n \right)^ n$ directly from $e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^ n$?
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?