Estimating Uncertainty in f(x)=a/x

[Niles]

Hi

Say I have a function given by f(x)=a/x, where a is some real constant. I know that there is some uncertainty Δx on x, but I don't know what it is. I just know that it will fluctuate around some value.

What is the proper way of determining how f(x) reacts to the uncertainty Δx? I mean, is there a way to find out if it is very sensitive to even small Δx or not?

 

[EnumaElish]

f(x) is sensitive to small Δx in the order -a/x² because Δf = f '(x)Δx = -(a/x²)Δx.

 

[Niles]

f(x) is sensitive to small Δx in the order -a/x² because Δf = f '(x)Δx = -(a/x²)Δx.

Thanks. Is Δf = f '(x)Δx a definition regardless of how f(x) depends on x?

 

[Niles]

Ok, I think I got it... Thanks!