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设z=(x+y)/(x-y),求dz
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设z=(x+y)/(x-y),求dz
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答案和解析
f(x)=z=x+y/x-y
dz=fxdx+fydy=[[(x-y)-(x+y)]/(x-y)^2 ]dx+[[(x-y)+(x+y)]/(x-y)^2]dy =-2y/(x-y)^2 dx+2x/(x-y)^2 dy =2/(x-y)^2 (xdy-ydx)
dz=fxdx+fydy=[[(x-y)-(x+y)]/(x-y)^2 ]dx+[[(x-y)+(x+y)]/(x-y)^2]dy =-2y/(x-y)^2 dx+2x/(x-y)^2 dy =2/(x-y)^2 (xdy-ydx)
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