Single-Variable Differentiation

Differential calculus is one of the most important tools of mathematical analysis. It was discovered in the seventeenth century by two famous scientists—the Englishman Isaac Newton and the German Georg Wilhelm Leibnitz—who discovered it independently of each other. The foundation of single-variable differential calculus is the concept of a derivative, which shows how a change in the independent variable affects the change in the functional value, that is, the change in the dependent variable. Since in economics it is very important to establish this type of relationship between economic variables, differential calculus plays an important role in economic theory. For example, it is important to know how a change in quantity will affect costs, how a change in price will affect profit, how a change in the money supply will affect inflation, etc. In this chapter, we define the term derivative, derive rules of differentiation and show how to calculate it. We show how derivatives can simplify the calculation of limits of the indefinite form 0/0 and ∞ $$\infty $$ / ∞ $$\infty $$ , that is, we present the L’Hospital rule. After that, we introduce higher-order derivatives and conclude by presenting some economic applications.