The derivative of the Floquet transform equals the Floquet tranform of the derivative. But can the Floquet tranform of the derivative of a function $f(r)$ can be expressed in terms of the Floquet tranform of the function $f(r)$?

So, is there a relation between $(U \frac{\partial f}{\partial r})(r)$ and $(Uf)(r)$ (like there is for the Fourier transform, i.e. $(F \frac{\partial f}{\partial r})(r)=iω(Ff)(r)$?

Many thanks in advance !

Jeff