They are all in good company in any century they choose. Glad you asked. Click Relate Those Rates to enlighten yourself. Now I suppose you want to know what you can do with antiderivatives as well. Click Riemann to scratch the surface of the answer to your question.
Derivatives exist for many more kinds of functions than just polynomial ones.
To explore the differentiability of the trig functions, click Trig to launch a study. Mathematicians often use the derivative to find a linearization to a function, particularly a difficult function. Sometimes the mathematician must use a special technique to evaluate a limit. For an example, click Sandwich Even though graphing calculators seem to be abundant these days, it still behooves the student of the calculus to know something about explaining the behavior of a curve by looking at its derivatives. There are only about 1 million places you can find on the net to continue your study of calculus.