DIFFERENTIAL CALCULUS

Vasileios Zikos

Chapter 2 in Essential Mathematics for Economics:A Student's Guide to Key Mathematical Techniques, 2026, pp 25-38 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After completing this chapter, students will be able to:Understand the concept of a derivative.Apply partial differentiation to various functions.Derive the total differential and total derivative of a multiple-variable function.Apply an implicit function theorem to compute partial derivatives.This chapter focuses on the study of differential calculus. One of the primary objectives is to find the derivative of a function, a process known as differentiation. The chapter also introduces the concept of the partial derivative, which describes the change in a function with respect to one variable while holding all others constant. Furthermore, the concept of the total derivative is discussed, which is relevant when there is a functional relationship among the independent variables of a function. Total derivatives consider all possible channels — both direct and indirect — through which the effect of an independent variable is transmitted to the dependent variable. Finally, this chapter presents an implicit function theorem and demonstrates how it can be applied to compute partial derivatives, including the slope of an indifference curve and the slope of an isoquant.

Keywords: Microeconomics; Applied Microeconomics; Optimization; First-order Conditions; Second-order Conditions; Equality Constraints; Inequality Constraints; Concavity; Convexity; Matrix Algebra; Determinants; Differential Calculus; Integral Calculus; First-order Linear Differential Equations; Utility Maximization; Profit Maximization; Research Applications (search for similar items in EconPapers)
JEL-codes: C01 C02 C61 D00 (search for similar items in EconPapers)
Date: 2026
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