Definition on my text book for differentiable is: for a point c, if
$f'(c) = \lim_{h \to 0} \frac{f(c+h) - f(c)}{h}$ , then f is differentiable at c
I'm confused that $f'(c)$ has a very similar definition which is also $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$. What is the difference between derivative and differentiate?