It is known that z=ln(xy+y? ), find the second partial derivative.

Solution: z=ln[y(x+y)]=lny+ln(x+y)

z/？ x = 1/(x+y)；

z/？ y =( 1/y)+ 1/(x+y)；

z/？ x？ =- 1/(x+y)？ ;

z/？ y？ =- 1/y？ - 1/(x+y)？ ;

z/？ x？ y=- 1/(x+y)？ .