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z'x=(-y/x^2)/(y/x)=-1/x z'y=(1/x)/(y/x)=1/y dz=z'xdx +z'ydy u=ln(x^2+y^2+z^2) u'x=2x/(x^2+y^2+z^2) u'y=2y/(x^2+y^2+z^2) u'z=2z/(x^2+y^2+z^2) du=2x/(x^2+y^2+z^2)dx + 2y/(x^2+y^2+z^2)dy + 2z/(x^2+y^2+z^2)dz
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