I believe that I may have once seen a definition of the derivative that went along these lines:
$f'(c)=\lim_{n\to\infty}\frac{f(x_n)-f(c)}{x_n-c}$
Here, $(x_n)$ is a sequence that converges to $c$.
As I do not recall much about it, I may have left out one or two important assumptions. However, does this seem in any way correct? And if so, does this theorem/etc. have a name? Thanks in advance!