Calling all statisticians.

[Borodog]

Consider the area of a square of width w +/- dw and height h +/- dh. We wish to calculate A = hw +/- dA. How do we calculate dA? Well, we can expect the actual value of A to lie in the range:

(w-dw)(h-dh) < A < (w+dw)(h+dh)

We could define a dA- to be hw - LHS and dA+ to be RHS - hw. Average the two and call it dA and you find:

dA = hdw + wdh.

Or,

dA/A = dw/w + dh/h

However, this is NOT the result of the magic formula-from-a-can for the propagation of uncertainty as annointed by some voodoo panel of statisticians somewhere:

(dA/A)^2 = (dw/w)^2 + (dh/h)^2

Now, I am fully confident that my derivation is somehow incorrect. I would just like to understand the logic behind the correct formula, since the derivation seems so simple.

Any help? The wiki article of propagation of uncertainty just gives the standard formulae, without elaborating on where they came from.