# Uncorrelated uncertainties

1. Jan 29, 2009

### bocobuff

1. The problem statement, all variables and given/known data
For uncorrelated uncertainties LaTeX Code: \\delta x and LaTeX Code: \\delta y give the values and uncertainties for W in standard format.
A.) W=x+y with x=4.2(0.2) and y=0.7(0.1)

2. Relevant equations

3. The attempt at a solution
well i think i am supposed to take the partial derivatives of W with respect to x and y (dW/dx and dW/dy) which both =1. Then is the total derivative DW/DXorY = 1+1 dx/dy? Or do I only use the derivatives for the uncertainties and just plug x and y, 4.2 and 0.7, into W?

2. Jan 30, 2009

### CompuChip

If you have a function $f(x_1, x_2, \cdots, x_n)$ where all the variables $x_i$ have their own uncertainty $\Delta x_i$, then what is the central value for f?
For the uncertainty there is a formula which involves the partial derivatives, but it's not what you seem to think it is. IIRC it is
$$(\Delta f)^2 = \sum_{i = 1}^n \left( \frac{\partial f}{\partial x_i} \Delta x_i \right)^2$$
but you can probably look that up in your textbook.