Question

高等数学，求下列函数的二阶偏导数，要详细过程及答案，急用，谢谢

Answer 1

已知z=ln(xy+y²)，求二阶偏导数缓闷
解：z=ln[y(x+y)]=lny+ln(x+y)
∂z/∂x=1/(x+y)；
∂z/∂y=(1/y)+1/(x+y)；
∂²z/∂x²=-1/(x+y)²；
∂²z/∂蚂族y²=-1/y²-1/(x+y)²；
∂²z/∂x∂y=-1/(x+y)²扰物弯.

Answer 2

z=ln(xy+y^2), z'让碧笑<x>=y/(xy+y^2), z'<y>慧漏=(x+2y)/(xy+y^2),
z''<xx>=-y^2/(xy+y^2)^2, z''<坦含xy>=z''<yx>=[xy+y^2-y(x+2y)]/(xy+y^2)^2=-y^2/(xy+y^2)^2,
z''<yy>=[2(xy+y^2)-(x+2y)^2]/(xy+y^2)^2=-(x^2+2xy+2y^2)/(xy+y^2)^2.