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设Z=arctan(y/x)的点m(1,1)处的全微分dz(1,1)为?
人气:351 ℃ 时间:2020-01-29 14:02:50
解答
Z=arctan(y/x)
zx=1/(1+(y/x)²) *(-y/x²)=-y/(x²+y²)|(1,1)=-1/2
zy=1/(1+(y/x)²) *(1/x)=x/(x²+y²)|(1,1)=1/2
dz(1,1)=-1/2dx+1/2dy
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