TITLE: Left Hand Derivative Definition
QUESTION [10 upvotes]: What is the actual definition of Left Hand Derivative?   
I bumped into this site and the second white box on their site gives the definition. Is that wrong?
What is the correct one then?

REPLY [16 votes]: The left-hand and right-hand derivatives of $f$ at $a$ are defined by
$$
f'_{-}(a)=\lim_{h\to 0^-}\frac{f(a+h)-f(a)}{h}
$$
and
$$
f'_{+}(a)=\lim_{h\to 0^+}\frac{f(a+h)-f(a)}{h}
$$
if these limits exist. Then $f'(a)$ exists if and only if these one-sided derivatives exist and are equal.