[微積] 偏微分
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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06/09 20:02, , 1F
06/09 20:02, 1F
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