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:

But would this mean that: ??

Or would the Y cancel out even in the uncertainty calculation leaving: ??

Thanks for any help you guys can offer!

-- Mike