Z=(X*X+Y*Y)/2Y在点(2,1)处的偏导数

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Z=(X*X+Y*Y)/2Y在点(2,1)处的偏导数
Z=(X*X+Y*Y)/2Y在点(2,1)处的偏导数

Z=(X*X+Y*Y)/2Y在点(2,1)处的偏导数
是全导还是对x,y的偏导
p表示偏导符号 ^2表示平方
pz/px = x/y
pz/py = (2y*2y-2*(x^2+y^2))/(4*y^2) = (y^2-x^2)/(2*y^2)
求全导将(2,1)代入,pz/px+pz/py得1/2

∵Z=(X^2+Y^2)/2Y=X^2/2Y+Y/2
∴dz/dx=(2x+ Y^2)/2Y=x/y+y/2
dz/dy= -X^2/(2*Y^2)+0.5
??故:?а(аz/аx)/ аy=-x/y^2+0.5
а(аz/аy)/ аx=-x/y^2
所以在点(2,1)处的偏导数
а(аz/аx)/ аy=-x/y^2+0.5=-1.5
а(аz/аy)/ аx=-x/y^2=-2

不是吧?

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