## Calculating Uncertainty from multiple variables

I have a questions about propogation of error.

I have two variables that are used to calculate the total value.
C = A * B
where
A = X * Y
B = Z / Y

So when substituting A and B to calculate C, the Y cancels and I am left with C = X * Z

But what if I know the total uncertainty of X, Y, and Z and I would like to calculate the uncertainty of C?

I am aware it must be done with:
$U_C = \sqrt{U_A^2+U_B^2}$

But would this mean that: $U_C = \sqrt{U_X^2+U_Y^2+U_Z^2+U_Y^2}$ ??

Or would the Y cancel out even in the uncertainty calculation leaving: $U_C = \sqrt{U_X^2+U_Z^2}$ ??