functions of several variables. For functions of several variables, we shall introduce “partial derivatives” , a generalization of the concept of “derivative” of real-valued function of one variable. Why should we consider functions of more than one variable? Let us consider a simple situation that will explain the need.
Suppose that a company is producing say pens and notebooks. This company is interested in maximizing its profit; then it has to find out the production level that will give maximum profit. To determine this, it has to analyze its revenue, cost, and profit functions, which are, in this case, functions of two variables (pen, notebook). Similarly, if we want to consider the volume of a box, then it will be a function of three variables namely length, width, and height.
Also, the economy of a country depends on so many sectors and hence it depends on many variables. Thus it is necessary and important to consider functions involving more than one variable and develop the “concept of derivative” for functions of more than one variable. We shall also develop the concept of “differential” for functions of two and three variables and consider some of its applications. In this chapter, we shall consider only real-valued functions.
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