 If we're doing this really carefully, we'd worry about the particular distribution of possibilities we'd have for our raw data, and we'd be able to convert that into a particular distribution for our possible results for our derived quantity. But we can get a good estimate by calculating this distance here. And that's just the difference between the values we would have got for y if we'd calculate it using the slightly high version of x, x plus delta x, compared to if we'd use just the expected value of x that we'd measured. So let's look at a few cases. Firstly, let's look at a linear multiplier. In other words, what if y is just some multiple of x? Then if we use this formula here, if we expand out this bracket, we're going to get lambda times x and lambda times delta x. And the lambda x is going to cancel with this lambda x, and we're just going to be left with the other term. So that makes sense. If I take 10 times a measurement, then I should multiply the measurement by 10, but I should also amplify my uncertainty by 10 as well. So if I had an uncertainty of a centimeter across a meter stick, then if I was talking about 10 of those, I'd have 10 meters is my average, but I'd also have now 10 centimeters is my uncertainty.