z=arctan(xy)的二次偏导数怎么求

2024-11-18 06:26:27
推荐回答(1个)
回答1:

∂z/∂x=[1/(1+(xy)²)]*y=y/(1+x²y²)
∂z/∂y=[1/(1+(xy)²)]*x=x/(1+x²y²)
求偏导数就像求导数一样,只需把其它变量看成常数即可:
Dz/Dx = {1/[1+(xy)²]}*y = y/[1+(xy)²],
D²z/DxDy = D(y/[1+(xy)²])/Dy