求偏导数或全导数1设z=(2x-y)^（2x-y）求xy的偏导

Question

求偏导数或全导数 1 设z=(2x-y)^（2x-y）求x y的偏导

Answer 1

z=(2x-y)^(2x-y)
lnz=(2x-y)ln(2x-y)
1,两边同时对x求导：
1/z*z'=2ln(2x-y)+2
z'=2z[ln(2x-y)+1]
即dz/dx=2(2x-y)^(2x-y)*[ln(2x-y)+1]
2,两边同时对y求导：
1/z*z'=-ln(2x-y)-1
z'=-z[ln(2x-y)+1]
即dz/dy=-(2x-y)^(2x-y)*[ln(2x-y)+1]
即dz/dx=(2x-y)^(2x-y)*[2ln(2x-y)+1]