What is the Joule-Thomson measurements uncertainty?

I will be measuring the Joule-Thomson coefficient for noble gases and I am trying to perform the uncertainty budget analysis prior to the measurements. However, I have my doubts here.

The JT coefficient is

$$mu_{rm JT} = left. frac{partial T}{partial p} right|_{rm h}.$$

The combined expanded uncertainty is defined as

$$U_{rm c} = k sqrt{sum^N_{i=1} left(frac{partial f}{partial x_i}right)^2 U^2(x_i)},$$

where $f$ is the JT coefficient in my case; $x_i$ is the measured property ($T_{rm in}$, $T_{rm out}$, $p_{rm in}$, $p_{rm out}$), $U$ is the single measurement uncertainty, $k$ is the coverage factor and $frac{partial f}{partial x_i}$ is the sensitivity coefficient of the measurement $x_i$.

The conditions will be kept constant at the entrance to the $Delta p$ imposing medium and will vary at the outlet, thanks to which I will follow the isenthalp and measure the integrated JT coefficient for each isenthalp from which I will later obtain the actual, local JT coefficients.

The question is: how to actually calculate the combined expanded uncertainty?

$$U_{rm c} = k sqrt{left(frac{partial mu_{rm JT}}{partial T_{rm in}}right)^2 U^2(T_{rm in}) + left(frac{partial mu_{rm JT}}{partial T_{rm out}}right)^2 U^2(T_{rm out}) + left(frac{partial mu_{rm JT}}{partial p_{rm in}}right)^2 U^2(p_{rm in}) + left(frac{partial mu_{rm JT}}{partial p_{rm out}}right)^2 U^2(p_{rm out})}$$

What is the significance of the following and how to calculate the sensitivity coefficients, e.g.,
$$frac{partial mu_{rm JT}}{partial T_{rm in}} = frac{partial frac{partial T}{partial p}}{partial T_{rm in}}$$

I may be wrong in my understanding here so any thoughts are appreciated!