Causal Noise Free 1st Order Derivative in Discrete Domain I need to have causal noise free first order derivation (Derivative).
Now I am using a simple finite differences formula:

$$ \frac{ x \left( n \right) - x \left( n - 1 \right) }{ {T}_{s} } $$

The filter above, being High Pass, is super sensitive to noise.
Do we have a noise free or noise reduced first order differentiation which does not need more than three point for calculation?
Well, Since basically the Derivative Operation is Linear Filter you can chose your own optimal trade off between Noise Sensitivity and Bandwidth.

If you look at Finite Differences Coefficients page at Wikipedia you can see you can chose higher "Accuracy" filters for 1st Derivative.
You can also chose Forward / Central / Backward method.