Outputting inequality with $e^x$ I many books I can find inequality which estimates $e$:
$$\left(1+\frac{1}{n}\right)^n \lt e \lt \left(1+\frac{1}{n}\right)^{n+1}$$
I am wondering if correct is also to write:
$$\left(1+\frac{1}{n}\right)^{nx} \lt e^x \lt \left(1+\frac{1}{n}\right)^{x(n+1)}$$
or maybe I can just raise the parties to the power?
Or maybe is any similiar inequality for $e^x$ like this?

yes for $x>0$, because taking something to the power of $x$ is a strictly increasing function.
http://www.lkozma.net/inequalities_cheat_sheet/ineq.pdf
To address your comment: here are some useful inequalities about the e, it is on the left of the first page.
