Let y = ln (XY) find the partial derivative ᦉ 8706; Z / ᦉ 8706; X

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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