In Calculus I and in most of Calculus II we concentrated on functions of one variable.  In Calculus III we will extend our knowledge of calculus into functions of two or more variables.  Despite the fact that this chapter is about derivatives we will start out the chapter with a section on limits of functions of more than one variable.  In the remainder of this chapter we will be looking at differentiating functions of more than one variable.  As we will see, while there are differences with derivatives of functions of one variable, if you can do derivatives of functions of one variable you shouldn’t have any problems differentiating functions of more than one variable.

Here is a list of topics in this chapter.

Limits  Taking limits of functions of several variables.

Partial Derivatives  In this section we will introduce the idea of partial derivatives as well as the standard notations and how to compute them.

Interpretations of Partial Derivatives  Here we will take a look at a couple of important interpretations of partial derivatives.

Higher Order Partial Derivatives  We will take a look at higher order partial derivatives in this section.

Differentials  In this section we extend the idea of differentials to functions of several variables.

Chain Rule  Here we will look at the chain rule for functions of several variables.

Directional Derivatives  We will introduce the concept of directional derivatives in this section.  We will also see how to compute them and see a couple of nice facts pertaining to directional derivatives.