求下列函数的二阶偏导数：(1)z=xy^2+x^3y (2)u=xLn(x+y)
问题描述：
求下列函数的二阶偏导数：(1)z=xy^2+x^3y (2)u=xLn(x+y)
答
那个符号用a表示了哈
(1)az/ax=y^2+3x^2y
az/ay=2xy+x^3
a^2z/ax^2=6xy
a^2z/(axay)=a^2z/(ayax)=2y+3x^2
a^2/ay^2=2x
(2)au/ax=ln(x+y)+x/(x+y)(=ln(x+y)+1-y/(x+y))
au/ay=x/(x+y)
a^2u/ax^2=1/(x+y)+y/(x+y)^2
a^2u/(axay)=a^2u/(ayax)=y/(x+y)^2
a^2u/ay^2=-x/(x+y)^2