偏導數 第二十六單元
Partial Derivative Definition
The Alternative Notations To find . We treat y as a constant and differentiate with respect to x To find . We treat x as a constant and differentiate with respect to y
Example
Geometric Interpretations of the Partial Derivatives
Geometric Interpretations of the Partial Derivatives
Example
Example
Example
High Order Partial Derivative
Example
Limit
Continuity at a Point
Example
Equality of Mixed Partials
Counterexample
Counterexample
Counterexample
Checking continuity at (0,0)
Dog Saddle
單元結語 以前考慮單變數函數時，變化只有一個方向(x軸)，因為現在考慮雙變數，固定了其中一個變數，於是出現了偏導數。 研究雙變數函數相關的章節，因為幾何意義為3D圖，這些需要讀者的體會及想像。
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