Z=ln(y/x)怎么求偏导数求z=x^(xy)的偏导数

Z=ln(y/x)怎么求偏导数求z=x^(xy)的偏导数
Z=ln(y/x)怎么求偏导数
求z=x^(xy)的偏导数

Z=ln(y/x)怎么求偏导数求z=x^(xy)的偏导数
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

z=ln(y/x)=lny-lnx
z'x=-1/x
z'y=1/y