What is the notation $f'(x^+) $ and $f'(x^-)$?

Question

Differentiability of a function at a point $x$ is confirmed when

$\lim_{h\to0} \frac{f(x+h)-f(x)}h$ exists and is finite.

But in some textbooks it is noted that a function is differentiable if $f'(x^+)$ and $f'(x^-)$ are equal and finite. I'm confused how this notation links with the above method of derivative by first principle.

Answer 1

Those are the left and right derivatives: $$ f'(x^+)=\lim_{h\to0^+}\frac{f(x+h)-f(x)}h,\ \ \ \ f'(x^-)=\lim_{h\to0^-}\frac{f(x+h)-f(x)}h. $$