z = xln(x + y)
∂z/∂x = ln(x + y) + x/(x + y)
∂²z/∂x∂y = ∂/∂y ln(x + y) + x•∂/∂y 1/(x + y)
= 1/(x + y) + x•(-1)/(x + y)²
= [(x + y) - x]/(x + y)²
= y/(x + y)²
z=xln(x+y),求z关于xy的二阶导数是
z = xln(x + y)
∂z/∂x = ln(x + y) + x/(x + y)
∂²z/∂x∂y = ∂/∂y ln(x + y) + x•∂/∂y 1/(x + y)
= 1/(x + y) + x•(-1)/(x + y)²
= [(x + y) - x]/(x + y)²
= y/(x + y)²