/sci/ - Science & Math

it's been a while since I've taken calc 3 or had to do anything with partial derivatives

for something of the form
[math]\frac{\partial y}{\partial x}dx[\math]
what is the meaning/significance behind the partial derivative being multiplied by the total differential(?) of the value in the "denominator"?
I have a faint buzzing in my head about the chain rule but I can't remember enough to really say