Re: [微分] 偏微分一題
※ 引述《Asbarla (木頭)》之銘言：
: g(t) = f( x(t), y(t) ) , find g''(t) ?
g(t) = f(x(t),y(t))
=> g = f(x,y) , x=x(t) , y=y(t)
dg dx dy
=> -- = fx * -- + fy * --
dt dt dt
2 2 2
d g dx dx d x dy dy d y
=> --- = fxx * -- * -- + fx * --- + fyy * -- * -- + fy * ---
2 dt dt 2 dt dt 2
dt dt dt
=> g''(t) =fxx(x(t),y(t))*(dx(t)/dt)^2 + fx(x(t),y(t))*x''(t) +
fyy(x(t),y(t))*(dy(t)/dt)^2 + fy(x(t),y(t))*y''(t)
--
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◆ From: 140.112.7.59
※ 編輯: bighead0720 來自: 140.112.7.59 (06/17 17:36)
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06/18 16:34, , 1F
06/18 16:34, 1F
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