CHAPTER 13 Partial Derivatives

CHAPTER 13 Partial Derivatives 13.1 Functions of Several Variables

Functions of Two Variables

Polynomial and Rational Functions

FIGURE 13.1.1 Domain of f in Example 2

Graphs FIGURE 13.1.2 Graph of a function of x and y is a surface

FIGURE 13.1.3 Graph of a polynomial function

FIGURE 13.1.4 Hemisphere in Example 5

FIGURE 13.1.5 Equipotential curves in Example 6

Level Curves FIGURE 13.1.6 Surface in (a) and level curves in (b)

FIGURE 13.1.6 Surface in (a) and level curves in (b)

FIGURE 13.1.7 Surface and level curves in Example 7

FIGURE 13.1.8 Graph of f(x, y) = 2sinxy in (a); level curves in (b)

FIGURE 13.1.9 Graph of f(x, y) = e-xsiny in (a); level curves in (b)

FIGURE 13.1.10 Contour map

FIGURE 13.1.11 Contour map showing the depth of ash around a volcano

Functions of Three or More Variables

FIGURE 13.1.12 Level surfaces in (a) of Example 9

FIGURE 13.1.13Level surfaces in (b) of Example 9

FIGURE 13.1.14Level surfaces in (c) of Example 9