Derivative of $\left | x-\left \lfloor x+1 \right \rfloor \right |$ at $x = 1.5$? Q: If $f(x)=\left | x-\left \lfloor x+1 \right \rfloor \right |$, where $\left \lfloor x \right \rfloor$ denotes the greatest integer less than or equal to x and $\left | x \right |$ denotes the absolute value of x, then $f'(1.5)$ =
I am not quite sure how the derivative of floor function and absolute function. I did some research and found out that the derivative of an absolute function is $\frac{\left \lfloor x \right \rfloor}{x}$. But I am stuck with the floor function.
What concept should I be aware of to solve this question?

$$f'(1.5)=\lim_{h\rightarrow0}\frac{|1.5+h-[2.5+h]|-|1.5-[2.5]|}{h}=$$
$$=\lim_{h\rightarrow0}\frac{|h-0.5|-0.5}{h}=\lim_{h\rightarrow0}\frac{0.5-h-0.5}{h}=-1.$$
