本論文是針對“多變數”（兩個以上）變數函數之導數而寫。長久以來多變數函數之導數均以偏導數代之，本論文則採取直接定義，這是以前不曾出現過的。因有了多變數函數之導數，其對應的多積分及各種有關多微積分的問題，也都可衍用單變數微積分的特性處理，使多微積分的問題變成簡單而易學。

How to define the fraction" f(x;y)-f(a;b) , where < x - a; y - b > represents an arbitrary vector? In this manuscript we try to exploit it directly as the definition of derivatives for two variable functions. Based on this concept we obtain various forms of the Mean Value(Vector) Theorems and the Fundamental Theorems of Calculus for multiple integrals. We hope they are able to be helpful for those people in learning and teaching multi-variable calculus.