This equation can be shown mathematically:
$\frac{\partial f}{\partial x}=\frac{2\pi i}{N} \mathcal F^{-1}\left(u\cdot \mathcal F(f(x,y)\right)$
I am struggling to understand the intuition behind it when talking about 2D fourier for images and the use of derivatives to detect edges.
How does multiplying the Fourier transform of the image with $u$ help us detect edges in the x direction? Why does it make the "edges" white and the rest of the image darker?
Any help would be appreciated. Thank you!