Question about the derivative definition The derivative at a point $x$ is defined as:
$\lim\limits_{h\to0} \frac{f(x+h) - f(x)}h$
But if $h\to0$, wouldn't that mean:
$\frac{f(x+0) - f(x)}0 = \frac0{0}$ which is undefined?

The definition $\mathbf{strictly}$ means $h\to 0$ and NOT $h=0$. Thats where you are mistaken. So you can't put $h=0$ directly in the formula, rather you have to calculate the limit of that expression for a particular $f(x)$ as $h\to 0$.
