Question

两个偏导数问题,求秒,1.z=(x-y)^u,u=x+y,求z分别对x和y的偏导数2.w=f(x,xy,xyz),求w对

Answer 1

1.取对数：

lnz=(x+y)ln(x-y)

对x求导：z'x/z=ln(x-y)+(x+y)/(x-y), 得：z'x=z[ln(x-y)+(x+y)/(x-y)]

对y求导：z'y/z=ln(x-y)-(x+y)/(x-y),得：z'y=z[ln(x-y)-(x+y)/(x-y)]

2. 令u=xy,v=xyz

则w=f(x, u, v)

w'x=f'x+f'u*u'x+f'v*v'x=f'x+f'u*y+f'v*yz

w'y=f'y+f'u*u'y+f'v*v'y=f'y+f'u*x+f'v*xz