Dy/dx in calculus

I don't get the concept of the notation dy/dx. Sometimes my physics teacher puts dx in the back of an equation and cross multiply with other number. Does this mean dx can be multiply like numbers? I just don't get the overall concept of dy/dx.

I'm in 3rd year calculus and I understand that derivative is the instantanous rate of change but how does it relates to the notation?

I hope I don't confuse you more (I'm not entirely certain myself).

The notation dy/dx comes from Leibniz's notation of derivatives. Originally, he used the Greek small delta (&delta;) which looks a bit like a 'd'. Anyway, the d or delta represents 'a small change in'. So dy/dx means 'the small change in y, with relation to x'.

Now the dy/dx notation has one useful property to it, and that is that it can behave as a fraction. Consider the Chain Rule:

dy/dx = dy/du * du/dx

The du's can cancel as though they were in fractions, to give you dy/dx again.

This becomes more pointed with differential equations and the relation with integration, where you can 'move' the dx to be able to integrate a DE.

I think that should about cover the very basic info about dy/dx notation... you'll probably get a better answer from a real mathematician...

Good luck.

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HallsofIvy