I have been wanting to ask this for a while. In Calc I, I was introduced to differentials. It seemed like they act like quantities(please corrected me if I'm wrong). For example dx/dx=1. You can obtain this by differentiating x or by eliminating the dx in the numerator and denominator(I do not know why this worked). What convinced me that differentials where quantities was the chain rule. dy/dx=(dy/du)(du/dx). The proof is a bit tough, but you will obtain the same result by eliminating the du.(I may be making a TREMENDOUS mathematical blunder here, but it seemes to work) In Calc III, I was introduced to [tex]\partial[/tex]x and[tex]\partial[/tex]y. Obviously I found out that [tex]\partial[/tex]x[tex]\neq[/tex]dx or else the chain rule for multiple variables would not simplify to dz/du. So, why are these two infinitesimals so different?