We study the mapping behavior of the Marchaud fractional derivative with different extensions in the scale of fractional weighted Sobolev spaces. In particular we show that the $α$--order Riemann--Liouville fractional derivative maps $W^{p,s}_0(Ω)$ to $W^{p,s-α}(Ω)$, for all $0<α<s<1$ and the $α$--order Marchaud fractional derivative with even extension maps the fractional Sobolev space $W^{p,s}((0,\infty))$ to $W^{p,s-α}(\real)$ for all $0<α<s<1$ and $ps\geq1$ . The proof is based on the Calderón--Lions interpolation theorem.