怎么求全微分z=f(x,x/y)

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怎么求全微分z=f(x,x/y)怎么求全微分z=f(x,x/y)怎么求全微分z=f(x,x/y)z=f(x,x/y)∂z/∂x=f1+f2/y∂z/∂y

怎么求全微分z=f(x,x/y)
怎么求全微分z=f(x,x/y)

怎么求全微分z=f(x,x/y)
z=f(x,x/y)
∂z/∂x=f1+f2/y
∂z/∂y=-xf2/y^2
dz=[f1+f2/y]dx+[-xf2/y^2]dy

az/ax=f1'+1/yf2'
az/ay=-x/y²f2'
所以
dz=az/axdx+az/aydy
=(f1'+1/yf2')dx-x/y²f2'dy