So I have been taught two formulas for error propagation:

For Z=A+B,

$\sigma_Z=\sqrt{(\sigma_A^2+\sigma_B^2)}$

and for Z=AB or Z=A/B

$(\dfrac{\sigma_Z}{Z})^2=(\dfrac{\sigma_A}{A})^2+(\dfrac{\sigma_B}{B})^2$

Are these not functions of 2 variables? Because I've also learnt the following:

$\sigma_Z=\dfrac{\partial Z}{\partial A}\sigma_A+\dfrac{\partial Z}{\partial B}\sigma_B$

So for example, which would I use for Z=A-8B?

So I have been taught two formulas for error propagation:

For $Z=A+B$,

$\sigma_Z=\sqrt{(\sigma_A^2+\sigma_B^2)}$

and for Z=AB or Z=A/B

$(\dfrac{\sigma_Z}{Z})^2=(\dfrac{\sigma_A}{A})^2+(\dfrac{\sigma_B}{B})^2$

Are these not functions of 2 variables? Because I've also learnt the following:

$\sigma_Z=\dfrac{\partial Z}{\partial A}\sigma_A+\dfrac{\partial Z}{\partial B}\sigma_B$

So for example, which would I use for $Z=A-8B$?