设z=z(x,y)由方程xyz+z^3=2确定,求Zx
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z=z(x,y)由方程x+y+z=sin(xyz)确定,求∂z/∂x.【你是要求z对x的偏导数,对吗?】
解:作函数f(x,y,z)=x+y+z-sin(xyz)=0
则∂z/∂x=-(∂f/∂x)/(∂f/∂z)=-[1-yzcos(xyz)]/[1-xycos(xyz)]
=[yzcos(xyz-1)]/[1-xycos(xyz)]
∂z/∂y=-(∂f/∂y)/(∂f/∂z)=-[1-xzcos(xyz)]/[1-xycos(xyz)]
=[xzcos(xyz)-1]/[1-xycos(xyz)]
解:作函数f(x,y,z)=x+y+z-sin(xyz)=0
则∂z/∂x=-(∂f/∂x)/(∂f/∂z)=-[1-yzcos(xyz)]/[1-xycos(xyz)]
=[yzcos(xyz-1)]/[1-xycos(xyz)]
∂z/∂y=-(∂f/∂y)/(∂f/∂z)=-[1-xzcos(xyz)]/[1-xycos(xyz)]
=[xzcos(xyz)-1]/[1-xycos(xyz)]
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