作者znmkhxrw (QQ)
看板Math
标题Re: [微积] 三变数的隐函数微分
时间Thu May 12 22:40:08 2011
※ 引述《sosick (钱钱)》之铭言：
: If the equation sin(x+y)+sin(y+z)=1 defines z implicitly
: as a differentiable function of x and y , evaluate (Ø^2 z÷ØyØx)
: Ø=partial的符号
: 拜托了 卡好久!!
sin(x+y) + sin(y+z)=1 (d是partial的符号)
partial derivative for x:
(A) cos(x+y) + (cos(y+z))*(dz/dx) = 0 → 解得 dz/dx
partial derivative for y:
(B) cos(x+y) + (cos(y+z))*(dz/dy) = 0 → 解得 dz/dy
由 (A) 再去对y做partial derivative 或是 由 (B) 再去对x做partial derivative
如果从 (A) 对y做的话
(-sin(x+y)) + (-sin(y+z))*(dz/dy)*(dz/dx) + (cos(y+z))*(d^2 z/dydx) = 0
这样就OK了
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◆ From: 114.25.176.22
1F：推 sosick :你到我那篇看一下答案!好像不太依样... 05/12 23:26
2F：→ znmkhxrw :........我算了一样阿= = 05/12 23:31
3F：推 sosick :是喔!!可是我算出来分母都是cos^2而已@@ 05/12 23:34
4F：→ znmkhxrw :先生你忘了(cos(y+z))*(d^2 z/dydx) 前面还有一个^^ 05/12 23:34
5F：→ sosick :我在算依次== " 05/12 23:35
6F：推 sosick :OK 会了!!感谢 知道错在哪儿了~ 05/12 23:40