Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?

Question

Define the function $f:(0,1)\to[0,1]$ where $f(x)=\{x\}$ is the fractional part of $x$. Am I correct in thinking that $f'(x)=1$ for $x\in(0,1)$? I'm asking because I think what I say is correct, but Mathematica 10 throws up other values, e.g.

N[FractionalPart'[9/10]] = 5.29432

EDIT

According to a member of the Mathematica team, they "...agree that that result from the derivative of FractionalPart doesn't really make sense. The symbolic derivative of FractionalPart hasn't really been implemented, so taking the numerical approximation doesn't return anything meaningful. There are developer reports on this issue so this functionality might exist in the future."

Answer 1

$\{x\}=x$ on $(0,1)$ so its derivative is 1.

Answer 2

I am assuming you mean f′(x)=1?

And yes you are correct in this thinking .

Answer 3

That is absolutely bizarre. I just confirmed your calculation in Mathematica 9. Even if I crank up WorkingPrecision, it doesn't give the expected result. Here is the output of

Plot[FractionalPart'[x], {x, 0, 2}, WorkingPrecision -> 100,
     MaxRecursion -> 8, PlotPoints -> 100, PlotRange -> {-2, 4}]

This is clearly incorrect.