u=f(r)计算得到，r对x的偏导数为rx=x/r∴u对x的偏导数为ux=f(r)·rx=f(r)·x/ru对x的二阶偏导数为uxx=f(r)·(x/r)+f(
u=f(r)计算得到，r对x的偏导数为rx=x/r∴u对x的偏导数为ux=f'(r)·rx=f'(r)·x/ru对x的二阶偏导数为uxx=f''(r)·(x/r)²+f'(r)·(r-x·rx)/r²=f''(r)·(x/r)²+f'(r)·(r²-x²)/r³同理，uyy=f''(r)·(y/r)²+f'(r)·(r²-y²)/r³uzz=f''(r)·(z/r)²+f'(r)·(r²-z²)/r³所以，uxx+uyy+uzz=f''(r)·(x²+y²+z²)/r²+f'(r)·(3r²-x²-y²-z²)/r³=f''(r)+2/r·f'(r)追问
谢谢啦
你给的答案感觉有点问题追问
恩恩就是这个 谢谢帮忙
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u=f(r)
计算得到，
r对x的偏导数为rx=x/r
∴u对x的偏导数为
ux=f'(r)·rx=f'(r)·x/r
u对x的二阶偏导数为
uxx=f''(r)·(x/r)²+f'(r)·(r-x·rx)/r²
=f''(r)·(x/r)²+f'(r)·(r²-x²)/r³
同理，
uyy=f''(r)·(y/r)²+f'(r)·(r²-y²)/r³
uzz=f''(r)·(z/r)²+f'(r)·(r²-z²)/r³
所以，
uxx+uyy+uzz
=f''(r)·(x²+y²+z²)/r²+f'(r)·(3r²-x²-y²-z²)/r³
=f''(r)+2/r·f'(r)追问
你给的答案感觉有点问题追问