Copyright © Johns and Bartlett ;滄海書局 CHAPTER 13 Partial Derivatives 13.3 Partial...
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Transcript of Copyright © Johns and Bartlett ;滄海書局 CHAPTER 13 Partial Derivatives 13.3 Partial...
Copyright © Johns and Bartlett;滄海書局
CHAPTER 13 Partial Derivatives
13.3 Partial Derivatives
2Copyright © Johns and Bartlett;滄海書局
Introduction
3Copyright © Johns and Bartlett;滄海書局
Computing a Partial Derivative
4Copyright © Johns and Bartlett;滄海書局
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Alternative Symbols
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Geometric Interpretation
9Copyright © Johns and Bartlett;滄海書局
FIGURE 13.3.1 Partial derivatives ∂z/∂x and ∂z/∂y are slopes of tangent lines to a curve C of intersection of the surface and a plane parallel to the x- or y-axes
10Copyright © Johns and Bartlett;滄海書局
FIGURE 13.3.1 Partial derivatives ∂z/∂x and ∂z/∂y are slopes of tangent lines to a curve C of intersection of the surface and a plane parallel to the x- or y-axes
11Copyright © Johns and Bartlett;滄海書局
12Copyright © Johns and Bartlett;滄海書局
13Copyright © Johns and Bartlett;滄海書局
14Copyright © Johns and Bartlett;滄海書局
FIGURE 13.3.2 Slope of tangent lines in Example 4
15Copyright © Johns and Bartlett;滄海書局
Functions of Three or More Variables
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18Copyright © Johns and Bartlett;滄海書局
Higher-Order and Mixed Derivatives
19Copyright © Johns and Bartlett;滄海書局
Alternative Symbols
20Copyright © Johns and Bartlett;滄海書局
Equality of Mixed Partials
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25Copyright © Johns and Bartlett;滄海書局
26Copyright © Johns and Bartlett;滄海書局