When I forget how to do a problem on a test, I usually get creative, often reteaching myself the lesson at the very last time, however I do occasionally get completely lost. I was supposed to use the derivative of a revenue function to find some final value of interest or something but there wasn't enough information I thought, so I got creative.

Now I knew that derivative=slope, but I never bothered to use the algebraic form until this occasion, where I made the derivative equation equal to the change in revenue over change in time and attempted to work with that (no luck though).

But, that lead me to my thought that the Leibniz's notation with it's "d"s might represent the delta of the x's and y's, I asked my calc teacher about this later and he confessed (despite his masters degree that he lords over us) that he didn't know if there was a connection and would have to ask one of the other teachers.

Now, unfortunately I am completely unable to read anything about mathematics online due to being easily confused by proofs with generic constants and such, can anyone tell me if there is a connection or anything?

The Leibniz notation simply relates an infinitesimal change in the numerator terms with respect to an infinitesimal change in the denominator term. The thing to remember is that the Leibniz notation is a ratio of 2 terms, which can each be manipulated algebraically. It is the rate of change of one variable with respect to another. A simple dy/dx term, for example, is found in differential equations and one of the techniques to solve a first order linear differential equation is to group all the x and y terms on either side of the = sign (this technique is called seperation of variables) and integrate. You'll also notice the dx term in an integral. The integral sign can be interpreted as "Take the sum of" and dx as "small increment in x direction".

dx is simply a tiny increment in the coordinate system. You have to understand all these small details about what the notation means if you want to have a chance in undertanding what the formulas mean. The formulas actually contain all the information about the variables and how they're related all you have to know is their notation and definitions. If you work some area or volume problems of varying geometries using integration the meanings become much more intuitive.

You are right, dy = [y(i+1)-y(i)], dx = [x(i+1)-x(i)] , and dy/dx = [y(i+1)-y(i)] / [x(i+1)-x(i)] but only if the two variables are linearly related otherwise there will be some error, because the derivative gives the slope of the line tangent to the point on a curve while the algebraic formula gives the slope of a secant line connecting two points lying on the curve. (Exact vs. approximate).

Don't know if that's what you were asking.

wow thats a complicated explanation for Leibniz notation. My calc teacher taught us that the 'd's simply stand for derivative. So: derivative of y over the derivative of x equals w/e. Hope that helps. I had calc last semester so Im a little more than rusty.