What is a differential calculus?

Answer 1

To a great extent, differential calculus is concerned with the slopes of curves - or with things that can be graphically represented as slopes, such as speed (the speed graph is a curve in a distance vs. time graph).

Answer 2

It is a branch of mathematics dealing with the rates of change - particularly the rate of change in one variable (y) associated with an increasingly small rate of change in the other (x).