Credentialism

I'm teaching an Industrial Organization class. It has a prerequisite of Intermediate Microeconomics, which has a prerequisite of Calculus I.

I have been showing them how to get from a demand equation to a marginal revenue equation. All hell has been breaking loose. Here are some of their problems:

• Some students can't take Q = 10 - P and solve for P. They just switch Q and P, which works in that example, but doesn't work with Q = 15 - 3P.
• Some students don't know the notation for a derivative. I write "dTR/dQ" and in their notes they write "2 TR/ 2Q".
• Some students don't recognize that a derivative is not a fraction. They read "dTR/dQ" as "the derivative of total revenue divided by the derivative of quantity."
• Some students don't know how to take the derivative at all. I tell them to use the chain rule and they wait for me to tell them what that is. I had to use the quotient rule last week and pandemonium ensued.
• Some students don't know how to solve for consumer surplus with a linear demand function and a given price. When I said, "It's the area of this triangle," they needed me to tell them the formula for the area of a triangle.

This is an upper-division course at a fully-accredited university. I don't know what to do. I'm not really in a position to fail everyone, job-security-wise. If I produce a class GPA substantially lower than 3.0, I'll have some 'splainin' to do. We've got to keep up the credentialism.