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?

For $x \in (1,2)$ we have $f(x)=\left | x-\left \lfloor x+1 \right \rfloor \right |=2-x$, so $f'(1.5)=-1$.
Same will be on any $(k,k+1)$ interval for $k \in \mathbb{Z}$.
