Differentiation of a constant function from first principles

Question

How do you differentiate a constant $K$ from first principles to show that it equals zero? $f(x) = K$ but what does $f(x+h)$ equal to where $h$ is the change in $x$?

Answer 1

If $f (x)=k $ for all $x $ then $f (x+h)=k $ also.

Answer 2

Your function $f$ is constantly equal to $K$.

This means that no matter what value $y$ you plug into $f$, it will always return $K$, i.e. $f(y)=K$. In particular, I can choose $y=x$ to get $f(x)=K$, or I can choose $y=x+h$ to get $f(x+h)=K$.