I was learning a bit of micro to help my brother and here is a bit of what I learned.

The economics term for derivative is marginal.  Marginal revenue is the derivative of the revenue function.  Revenue is defined by R(q) = P(q)*q the price at a particular quantity times the quantity sold.  So, R'(q) = P'(q)*q + P(q) is the marginal revenue.  Usually P(q) does not change so P'(q) is zero. Therefore, R'(q) = P(q).  So, marginal revenue is the price I charged for producing one unit (remember P(q) is constant for any q).

Can also have marginal cost.  Which is similar to marginal revenue.

I also learned about elasticity.  Elasticity is the percent that Y changes in response to X changing by 1%.  In general elasticity is define by e = (dY/dX)*(X/Y).  This says the elasticity of Y with respect to X is the derivative of Y with respect to X times X over Y.  So, elasticity is a general thing you calculate for anything.  You just plug the words in for Y and X.  For example, the elasticity of demand with respect to price is: n = (dQ/dP)*(P/Q).  However, the demand curve usually has a negative slope so the derivative is negative.  Economists don’t like the negative so they usually write the elasticity of demand as n = -(dQ/dP)*(P/Q).  Remember D'(p) = (dQ/dP) and D(P) = Q = some equation in terms of P.  Usually, we like our equations to be in terms of one variable so I would substitute like this: n = -(dQ/dP)*(P/D(P)).  So, what does elasticity of demand tell us?  Well, first demand tells us how much a consumer buys at a particular price.  Elasticity looks at how the quantity changes as price changes.  So, 0<=n<1 if the demand for a good at that price is inelastic.  Meaning the quantity demanded doesn’t change radically.  If n > 1 then the demand is elastic meaning if we change the price the demand will change quite a bit.

Another interesting thing I learned was about the market demand residual.  This starts to be interesting because it is taking into account other (possibly identical) businesses.  The market demand residual is defined as Dr(P) = D(P) – So(P) where So(P) is the supply of all the other businesses that are identical and D(P) is the demand of the business that is being examined.  So, if there are n identical business then So(P) = sum(i = 1 to n-1) of Si(P).