求题中二次导数和值过程，答案是f"（r）+2/r*f'（r）
2个回答
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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)
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)
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谢谢啦
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