[dls2016]

A quick intuition for this is: d/dx(e^(iwx)) = iw*e^(iwx)... that is, differentiation amplifies higher frequencies more than lower ones.

[aidenn0]

Right, an integral is a low-pass filter with infinite gain at DC and a derivative is a high-pass filter with gain of 0 (negative infinity dB) at DC; they both have 90 degrees of phase shift.