I am collecting some easy problems for my students and now I am facing to the following problem:
Prove that the function $f(x)=\left(1+\frac{1}{x}\right)^x$ is increasing in $(0,+\infty)$.
Undoubtedly, they will solve it by using the logarithmic differentiation. I am wonder what can I do if someone wants me to verify it just by doing the definition of increasing function? I think , I am missing somethings here around. Light my way. Thanks!