Why taking derivative amplifies noise
Differentiation in one axis will amplify high-frequency components. Assuming noise at Fs/2 (i.e maximum frequency), the gain at this frequency will be 6 dB. Intuitively, if you have a sequence alternating between +1 and -1 i.e (1, -1, 1, - 1), Then the difference will be +2, - 2, +2, -2, a gain of 6 dB

Another reason is that by differentiating, you remove the low-frequency components, so your eyes see mostly the high-frequency components giving you the impression of having more noise.