I have $f(x)=(1+\frac{1}{x})^{x}$, I need to find the derivative of this, using the definition of derivative, and show that f is monotonically increasing.
Using the definition, I have that $\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h} = \lim_{h\rightarrow0}\frac{(1+\frac{1}{x+h})^{x+h}-(1+\frac{1}{x})^{x}}{h}$ whose numerator is the same as $(1+\frac{1}{x+h})^{x}(1+\frac{1}{x+h})^{h}-(1+\frac{1}{x})^{x} $
At this point, I'm not sure how to proceed. Would I need to use binomial formula?