Re: [微分] 偏微分一題

[bighead0720 (ocean)]

※ 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)
推 Asbarla:了解，謝謝