[微積] 偏微分

[silentchaos (眷戀)]

let x=r^2+s^2 y=2rs and z=(x,y) zrr=?

Zr=(Zx)(Xr)+(Zy)(Yr) (chain rule)
  =2(r(Zx)+s(Zy))

and d/dr=2(r*d/dx+s*d/dy)

hence Zrr=(d/dr)*(dZ/dr)=2(r*d/dx+s*d/dy)(2(r(Zx)+s(Zy))

ie Zrr=4(r^2*(Zxx)+2rsZxy+s^2*Zyy)

but the ans in textbook is

Zrr=4(Zx+r^2*(Zxx)+2rsZxy+s^2*Zyy)
      ^^
     extra term

just ask if my calculation have mistakes?

THX~

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