求z=ln(x*x+y*y)的二阶偏导数

2024-11-22 21:10:02
推荐回答(1个)
回答(1):

∂z/∂x=2x/(x²+y²)
∂z/∂y=2y/(x²+y²)
∂²z/∂x∂y=[2(x²+y²)-2x*2y]/(x²+y²)²=2(x-y)²/(x²+y²)²
∂²z/∂x²=∂[2x/(x²+y²)]/∂x=[2(x²+y²)-2x*2x]/(x²+y²)²=2(y²-x²)/(x²+y²)²
同理∂²z/∂y²=2(x²-y²)/(x²+y²)²