In this chapter, we will learn the crucial and elegant theorem provided by Euler. We will also learn a few deductions from it and also how to apply them to obtain Partial Derivatives of functions apparently in the complex form in a very simple way.

A function f(x, y, z) is called a Homogeneous functions of degree n if by putting X = xt, Y = yt, Z = zt, then the function becomes tⁿ.f(x, y, z) i.e.

f(xt, yt, zt) = t^n.f(x, y, z)

This chapter is further divided into the following 4 categories:

• Class A: Problems based on Euler’s theorem for Homogeneous function


• Class B: Problems based on Euler’s theorem Corollary 1


• Class C: Problems based on Euler’s theorem Corollary 2


• Class D: Problems based on Euler’s theorem Corollary 3