※ 引述《iamagine (A-gine)》之銘言：
: Theorem11.15
: Let V be open set in |R^n
: Let a E V (a屬於V)
: Let f:V→|R^m
: If all first-order partial derivatives of f exist in V and are continuous at
: a,
: Then f is differentiable at a.
: 這裡的條件是要first-order partial derivatives在a點
: 不僅僅要存在，而且first-order partial derivatives在a點還要連續.
: 我想問的是，為什麼定理15的條件要強到：它偏導數在a點要連續?
: 只是存在的話，f在a點就不可微了嗎?
: (如果可以，能不能麻煩大大舉實際的例子跟我說>""<)
yes
Consider the function f(x,y) = sign( xy )
fx and fy exists and are both 0 at (0,0) while f is not continuous at (0,0)
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