NEKG33 Mathematical methods for economists

Chapter 9 : Day 09: Partial derivatives

By Lund University

Ordinary derivatives are for newbies. Today we move on from functions of a single variable to functions of several variables and do partial derivatives.

Functions of two variables

In this section we investigate functions z = f(x,y).

Problem: Evaluate a function of two variables

Problem: Evaluate a function of two variables

Partial derivatives

For a function of two variables, we can define two derivatives, one for each variable. Such derivatives are called partial derivatives. Similarly, we get 4 second order partial derivatives.

Partial derivatives, rough introduction

Partial derivatives: Problems

Exercises on partial derivatives.

Problem: Find partial derivatives

Problem: Find partial derivatives

Problem: Find first- and second-order partial derivatives

Problem: Find first- and second-order partial derivatives

Problem: Find first- and second-order partial derivatives