设z等于ln(x2+y2),求在(1,-1)处的二阶偏导数

设z等于ln(x2+y2),求在(1,-1)处的二阶偏导数
2025-04-11 09:23:43
推荐回答(1个)
回答1:

z=ln(x²+y²)
∂z/∂x=2x/(x²+y²)
∂z/∂y=2y/(x²+y²)
∂²z/∂x²=[2(x²+y²)-2x·2x)]/(x²+y²)²=(2y²-2x²)/(x²+y²)²
∂²z/∂x²=-2x·2y/(x²+y²)²=-4xy/(x²+y²)²
∂²z/∂y²=[2(x²+y²)-2y·2y)]/(x²+y²)²=(2x²-2y²)/(x²+y²)²