Derivatives of functions are used to study the “rate” of change — that is, how fast or how abruptly something changes. The word “rate” can be understood very broadly: from the mechanical speed of a car to sudden changes in stock market prices.

The ability to compute derivatives is a fundamental skill for anyone who wants to learn mathematics beyond high school level — and, quite frankly, to move mathematically beyond the 17th century. And, of course, to pass pretty much any mathematics course at university.