z = xy/[(x^2+y^2)^1/2]u=xyv=x^2+y^2z=u/v^(1/2)∂z/∂x = [u'(x)v^0.5 + u(v^0.5)']/v = [yv^0.5+xyx/(x^2+y^2)0.5/v= (2x^2+y^2)y/[(x^2+y^2)^1.5]∂z∂y = (2y^2+x^2)x/[(x^2+y^2)^...为什么我算的是dz = [y^3 dx + x^3dy] / (x^2+y^2)^1.5 ？？检查了一下：您的对：∂z/∂x = [u'(x)v^0.5 + u(v^0.5)']/v = [y(x^2+y^2)^0.5- x^2y/(x^2+y^2)0.5/(x^2+y^2)= (y^2)y/[(x^2+y^2)^1.5] = y^3/(x^2+y^2)^1.5∂z∂y = (x^3)x/[(x^2+y^2)^1.5]dz = (y^3 dx + x^3 dy) / (x^2+y^2)^1.5