Finding $\frac{\mathrm d}{\mathrm dx}(6)$ by first principles I had an exercise in my text book:

Find $\frac{\mathrm d}{\mathrm dx}(6)$ by first principles.

The answer that they gave was as follows:
$$\lim_{h\to 0} \frac{6-6}{h} = 0$$
However surely that answer would be undefined if we let $h$ tend towards $0$, as for finding all other limits like that we substitute $0$ in the place of $h$? 

The answer is right. We know that if the following limit $$\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$ exists, then it is denoted by $f'(x)$. In the case $f$ is a constant function, the numerator of previous fraction in limit is absolutely zero but the variable $h$ in the denominator is going to zero but it is not zero. We know many functions that $x=0$ is excluded from their domains but we prove their limit at zero.
