麻烦求该函数的一阶和二阶偏导数？谢谢回答

Question

如题所述

Answer 1

先求dz/dx

两边对x求偏导
2z*dz/dx-y+dz/dx=0

dz/dx=y/(2z+1)
再求dz/dy
同理
dz/dy=x/(2z+1)

然后
d^2z/dxdy=d/dx(dz/dy)=d/dx[x/(2z+1)]

dx/dx *(2z+1) - x*d(2z+1)/dx
= ----------------------------------------------
(2z+1)^2

(2z+1) - x*2*dz/dx
= ------------------------------
(2z+1)^2

(2z+1) - 2xy/(2z+1)
= -----------------------------------
(2z+1)^2

(2z+1)^2- 2xy
= ----------------------
(2z+1)^3