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If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x". Here we look at doing the same thing but using the "dy/dx" notation (also called Leibniz's notation) instead of limits. Here I introduce differentiation, dy/dx as used in calculus. This video explains the difference between dy/dx and d/dx Learn Math Tutorials Bookstore. dy divided by dx generally represents the rate of change or slope. (4) Even within pure mathematics itself, we need a definition of dy/dx that can be applied when y is not a function of x.