Left-hand and Right-hand Derivatives

Left-hand derivative (LHD):
$$ \mathrm{LHD} = \lim_{h \to 0^-} \frac{f(c+h) - f(c)}{h} $$
Right-hand derivative (RHD):
$$ \mathrm{RHD} = \lim_{h \to 0^+} \frac{f(c+h) - f(c)}{h} $$
Differentiability ⇔ LHD = RHD (finite and equal).