求下列函数的二阶偏导数 1）z=x^4+3*x^2*y+y^3 2）z=xln(x+y)求下列函数的二阶偏导数1）z=x^4+3*x^2*y+y^32）z=xln(x+y)

zx=4x^3+6*xy
zy=3*x^2+3y^2
(2)
zx=ln(x+y)+x/(x+y)
zy=x/(x+y)

1）z=x^4+3*x^2*y+y^3
∂z/∂x=4x^3+6yx
∂²z/∂x∂y = 0+6x
2）z=xln(x+y)
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=x^4+3x²y+y³
∂z/∂x = 4x³+6xy
∂z/∂y = 3x²+3y²
∂²z/∂x² = 12x²+6y
∂²z/∂x∂y = 6x
∂²z/∂y² = 6y
----------------------------
z=xln(x+y)
∂z/∂x = ln(x+y) + x/(x+y)
∂z/∂y = x/(x+y)
∂²z/∂x² = 1/(x+y) + [(x+y)-x]/(x+y)² = 1/(x+y) + y/(x+y)² = (x+2y)/(x+y)²
∂²z/∂x∂y = 1/(x+y) - x/(x+y)² = y/(x+y)²
∂²z/∂y² = - x/(x+y)²