由轮换对称性,只需要计算αf/αx,α^2f/αx^2 即可,把x换作y就是另一个偏导数
r对x的偏导数是x/r,所以
αf/αx=g'(r)×x/r
α^2f/αx^2=g''(r)×(x/r)^2+g'(r)×[r-x×(x/r)]/r^2=g''(r)×x^2/r^2+g'(r)×[r^2-x^2]/r^3
所以,α^2f/αx^2=g''(r)×y^2/r^2+g'(r)×[r^2-y^2]/r^3
所以,α^2f/αx^2+α^2f/αx^2=g''(r)+g'(r)/
由轮换对称性,只需要计算αf/αx,α^2f/αx^2 即可,把x换作y就是另一个偏导数
r对x的偏导数是x/r,所以
αf/αx=g'(r)×x/r
α^2f/αx^2=g''(r)×(x/r)^2+g'(r)×[r-x×(x/r)]/r^2=g''(r)×x^2/r^2+g'(r)×[r^2-x^2]/r^3
所以,α^2f/αx^2=g''(r)×y^2/r^2+g'(r)×[r^2-y^2]/r^3
所以,α^2f/αx^2+α^2f/αx^2=g''(r)+g'(r)/