Re: [微積] Total diff + Tangent plane

[Honor1984 (希望願望成真)]

※ 引述《subtropical (風大雨大)》之銘言：
: f:  D   ->    R
:   (x,y) -> xy^(1/3)    , x>0, y>0
: 求(1,1)的全微分


df = y^(1/3)dx + (1/3)xy^(-2/3)dy

df|       =  dx + (1/3)dy
   (1,1)


: 求(1,1,1)的Tangent plane

z = xy^(1/3)

g(x,y,z) = z - xy^(1/3)

▽‧g|  = (-y^(1/3),-(1/3)xy^(-2/3),1)|
      (1,1,1)                          (1,1,1)

        = (-1, -1/3, 1)


Tangent plane

-(x-1)-(1/3)(y-1)+(z-1) = 0


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