高数（5）.. 20
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(5) z = (1+x/y)^(x/y), lnz = (x/y)ln(1+x/y)
z'<x>/z = (1/y)ln(1+x/y) + (x/y)(1/y)/(1+x/y)
z'<x> = z[(1/y)ln(1+x/y) + (x/y)/(x+y)],
z'<y>/z = (-x/y^2)ln(1+x/y) + (x/y)(-x/y^2)/(1+x/y)
z'<y> = -z[(x/y^2)ln(1+x/y) + (x^2/y^2)/(x+y)],
x = y = 1 时 z = 2，
z'<x> = 2(ln2 + 1/2) = 1+2ln2
z'<y> = -2(ln2 + 1/2) = -(1+2ln2)
dz = (1+2ln2)(dx-dy)
z'<x>/z = (1/y)ln(1+x/y) + (x/y)(1/y)/(1+x/y)
z'<x> = z[(1/y)ln(1+x/y) + (x/y)/(x+y)],
z'<y>/z = (-x/y^2)ln(1+x/y) + (x/y)(-x/y^2)/(1+x/y)
z'<y> = -z[(x/y^2)ln(1+x/y) + (x^2/y^2)/(x+y)],
x = y = 1 时 z = 2，
z'<x> = 2(ln2 + 1/2) = 1+2ln2
z'<y> = -2(ln2 + 1/2) = -(1+2ln2)
dz = (1+2ln2)(dx-dy)
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