Is there a closedform expression for the Floquet transform of the derivative of a function $f$ (analog to the wellkown property of the Fourier transform)?

If I'm not mistaken, the definition of the Floquet transform is $(Uf)(r)=\sum_{R\in L}e^{ik\cdot R}f(rR)$, where the sum runs over vectors $R$ on a $d$dimensional periodic lattice $L$. The vector $k$ is fixed. Now I just take the derivative of both sides with respect to $r$, $\frac{\partial}{\partial r}(Uf)(r)=(U\frac{\partial}{\partial r}f)(r)$. In words: the derivative of the Floquet transform is the Floquet transform of the derivative. 

