Reddit reviews Families of Curves and the Origins of Partial Differentiation

Partial derivatives were invented by Leibniz as a result of Johann and Jakob Bernoulli's studies of a practical problem: the Brachistochrone problem. There's a very good book by Steven Englesman, unfortunately very expensive, that discusses all this in detail (especially in Chapter 2). I think it's useful to know the origins of the idea, even though partial derivatives are used somewhat differently now (at least in Calc III).