Re: [微積] 三變數的隱函數微分
※ 引述《sosick (錢錢)》之銘言：
: 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的符號
: 拜託了 卡好久!!
sin(x+y) + sin(y+z)=1 (d是partial的符號)
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) 再去對y做partial derivative 或是 由 (B) 再去對x做partial derivative
如果從 (A) 對y做的話
(-sin(x+y)) + (-sin(y+z))*(dz/dy)*(dz/dx) + (cos(y+z))*(d^2 z/dydx) = 0
這樣就OK了
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