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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)=?

OCW Scholar - Single Variable Calculus
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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.
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!

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