Question

I'm not sure how Δx works when it's being multiplied.

Ex. (x+Δx) (x+Δx)= ???

What does x(Δx)=?
Would it be Δx^2
But then.. what does Δx(Δx)=?

Answer 1

I think ∆x∆x is called the second order small change and as ∆x→0 it goes to 0, Prof Strang calls it 'nothing of nothing' where as x(∆x) is 'nothing of something' which is the ratio that we have to preserve in taking the limit. But that's just how I see it.

Answer 2

Thanks =) Wasn't quite what I was looking for, but in reframing my question.. I figured it out.
x(Δx)= xΔx
Δx(Δx)=Δx^2

That's what I got stuck on. Was looking at this derivatives formula that kept skipping the step where they added the two xΔx's to get 2xΔx... I kept thinking.. where did the 2x come from?? anyways, thanks!