1. Section 13.3 Partial Derivatives

3. To find you consider y constant and differentiate with respect to x. Similarly, to find you hold x constant and differentiate with respect to y. Examples:

4. Geometrically speaking, the partial derivatives of a function of two variables represent the slopes of the surfaces in the x- and y- directions.

5. No matter how many variables are involved, partial derivatives can be thought of as rates of change. Example: Consider the Cobb-Douglas production function When x=1000 and y=500, find a. The marginal productivity of labor b. The marginal productivity of capital. Assume x represents labor, and y capital.

6. As we can do with functions of a single variable, it is possible to take second, third, and higher partial derivatives Notation:

7. Examples: 1) Find the first four second partial derivatives.