Let $n \in \mathbb{N}$. For $x,y,\eta \in \mathbb{R}^n$ and a multi-index $\alpha = (\alpha_1,\dots,\alpha_n) \in \mathbb{N}_0^n$, use the conventions $|\alpha| := \alpha_1 + \cdots + \alpha_n$, $(y-x)^\alpha := \prod_{j=1}^n (y_j-x_j)^{\alpha_j}$, and $\partial_\eta^\alpha := \partial_{\eta_1}^{\alpha_1}\cdots \partial_{\eta_n}^{\alpha_n}$. Define $D_\eta^\alpha := (-i)^{|\alpha|}\partial_\eta^\alpha$. Then

\begin{align*} D_\eta^\alpha e^{i(y-x)\cdot \eta} = (y-x)^\alpha e^{i(y-x)\cdot \eta}. \end{align*}