My question is similar to this question, though a bit more specfic. In a nutshell: any good books that look at the calculus behind economics?
Motivation: I teach a high school course called "Business Calculus," which is essentially a calculus course with business and economics applications. It's aimed at high school seniors who have struggled with math in the past.
The textbook tends to introduce math abstractly (here's the chain rule) and then give an application (here's how you use it). I'm trying to flip that: here's a situation; let's figure out some tools to help us address it.
For example, to introduce the chain rule, I wrote an exploration where revenue is a function of price and quantity (R=p*q), which are themselves a function of number of employees. The Marginal Product of Labor is a derivative of revenue with respect to number of employees, so students had to figure out and apply the chain rule in order to calculate MPL, which in turn had consequence for workers' wages.
Problem is that right now I know very little about the calculus of econ except what I can glean from my textbook's word problems and whatever research I can do on the internet. I'd desperately love a recommendation for a book that either teaches calculus from an econ perspective, or teaches econ from a calculus perspective.