Question

suppose that some quantity y is a function of some other quantity x, and suppose that y is a mass, i.e. y is measured in pounds, and x is a length, measured in feet. What units do the increments △y and △x, and the derivative dy/dx have?

Answer 1

△y is mass gain. Like when you say: "I gain 5 pounds in weight". So 5 pounds is △y in this case.
Simmilar story for △x.
dy/dx = △y/△x for △y and △x very, very, very... small. So pounds/feet