College physics: error propogation using partial derivatives?

I'm not real sure about how to do this. For our experiment, we determined the spring constants for a bunch of springs several different ways: 1) F=kx, measuring the force mg on the spring and x, the change in the length %26amp; 2) finding the period and mass



So, for example, say that this was our data for the first method:

total mass: 0.149 kg (+ or - 0.002 kg)

x1: 0.14 m (+ or - 0.03 m)

x2: 0.38 (+ or - 0.03 m)

x2-x1: 0.245 m



Doing the algebra, k = (mg)/x. So our spring constant was 6.0 N/m. How do we factor error into this? For our x2-x1, how do we add up the error, or don't we? And how do you evaluate the expression he gave us for the error for k:



(delta k)^2 = ((partial deriv k/partial deriv m)(delta m))^2 + ((partial deriv k/partial deriv x)(delta x)^2



Not really sure what to do about the partial derivatives. Thanks for any help, explanations, or tips in advance! :DCollege physics: error propogation using partial derivatives?
First let's figure out the uncertainty in x2-x1. Let x=x2-x1

未x=sqrt((未x2)虏+(未x1)虏)

未x=0.0424



The general formula for error propagation is, as you stated above:

未k=sqrt(((鈭俴/鈭俶)*未m)虏 + ((鈭俴/鈭倄)*未x)虏)



To find the partial derivative of k with respect to m, just treat g and x as constants:

鈭俴/鈭俶=g/x

Do the same for x:

鈭俴/鈭倄=-mg/x虏



Now plug in the values for m, g, x, and their uncertainties into the equation above

未k=1.0352, or with sig figs 1.0