calculus - How do you prove $x^{x+1}>{(x+1)}^x, x>c$?

It is visible the left side is bigger simply because it's a higher power but calculating the first derivatives leads back to almost the same inequivalence. I tried to prove it with induction which also didn't quite lead anywhere. Any ideas?

Edit: c is some constant. If it's a problem, use c=3 (it's slightly less I believe but definitely >2).

Answer

If you mean to prove it for $x>e$, so prove that $f(x)=\frac{\ln x}{x}$ is a decreasing function for $x>e$.