1. ## What is dx/x?

I'm pretty rusty coming back to calculus after a while (and was never hugely solid) but I've hit a wall on something that is probably really obvious. It's from some economics I'm trying to understand: "dx/x" keeps on cropping up. Example:

"We denote relative changes by a tilde: x-tilde = dx/x."

And a differentiation they're using to investigate local stability contains several of these terms e.g. dI/I, d-lambda/lambda etc.

But what does it mean? A small change in x with respect to x? But how does that make any sense?

If a fuller example is needed, I can provide a more detailed write-up. I can't find any answer on the interweb or in my physics course unit notes. I thought it might be linearisation or taylor approximation related, but it doesn't seem to be (though in one version of the problem, linearisation is mentioned.)

Thanks and apologies if this is a really dumb question...

2. ## Re: What is dx/x?

Hmm, OK, I think I see. So a new quote: “a 1% change in manufactures (dY/Y) causes a 1/Z (>1) percent change in employment.”

So if dividing by Y can be a reasonably large number (1/100), that means dY is not a differential. If it was, the result would be as close to zero as makes no odds. But that at least explains what it is: a change proportional to its current value. Still seems very odd to me.

Does that sound right? It seems mathematicall unsound: to know that it's a 1% change, you need to make the change at t+1 and compare to what Y was at t. I guess this is convenient shorthand, but is this common notation?

3. ## Re: What is dx/x?

I would call that "relative change"- how much a quantity changes compared with the quantity itself.

4. ## Re: What is dx/x?

I don't want to go in depth with question but I want to tell something about dx as-when a differential is defined, all of a sudden the dx has a meaning, but then when an integral is being evaluated.
bay s theorem

5. ## Re: What is dx/x?

Originally Posted by manoj9585
I don't want to go in depth with question but I want to tell something about dx as-when a differential is defined, all of a sudden the dx has a meaning, but then when an integral is being evaluated.
bay s theorem
No, this has nothing to do with integrals. Differentials are used in many other problems than just integrals- although that is the simplest use. Dano said in his first post, "We denote relative changes by a tilde: x-tilde = dx/x." If x= 100 and then increases by dx= 1, from 100 to 101 the relative change is $\frac{1}{100}$, it has changed by 1%. If x= 1000 and then increases from 1000 to 1010, dx= 10 and we still have dx/x= 10/1000= 1/100= .01 or 1%.

6. ## Re: What is dx/x?

Thanks man, you correct my post.