Question

求二元函数z=x^2ye^y的二阶偏导数

Answer 1

z=x²ye^y

那么

∂z/∂x=2xye^y

∂z/∂y=x²e^y +x²ye^y

所以

二阶偏导数为

∂²z/∂x²=2ye^y

∂²z/∂x∂y=2xe^y +2xye^y

∂²z/∂y²=x²e^y +x²e^y +x²ye^y=2x²e^y +x²ye^y