Finding the derivative of f(x)=5 using the limit process

[latex]f(x)=5[/latex] [latex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h=\lim_{h\to0}\frac{5-5}h=\lim_{h\to0}\frac0h=0[/latex] which is to be expected - a constant function never changes, so its derivative must be zero everywhere.