In the book of Helgason which is called "Radon transform and integral geometry", he defines on page 2 the Radon transform on hyperplanes as:
$$ \hat{f}(\xi) = \int_{\xi} f(x) dm(x)$$
Where $dm(x)$ is a Euclidean measure on the hyperplane $\xi$.
Now, on page 3, he writes down that: $$(2) \hat{\left(\frac{\partial f}{\partial x_i}\right)}(\omega , p) = \omega_i \frac{\partial \hat{f}}{\partial p}(\omega , p)$$
where $\xi$, can be written as: $\xi \{ x \in \mathbb{R}^n : <x,\omega> = p \}$, where $<,>$ is the standard inner product of the Euclidean space.
I don't understand how did he arrive at equation $(2)$, anyone can help me on this?