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)
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![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)](/uploads/image/z/8708414-14-4.jpg?t=%E6%B1%82%E4%B8%8B%E5%88%97%E5%87%BD%E6%95%B0%E7%9A%84%E4%BA%8C%E9%98%B6%E5%81%8F%E5%AF%BC%E6%95%B0+1%EF%BC%89z%3Dx%5E4%2B3%2Ax%5E2%2Ay%2By%5E3+2%EF%BC%89z%3Dxln%28x%2By%29%E6%B1%82%E4%B8%8B%E5%88%97%E5%87%BD%E6%95%B0%E7%9A%84%E4%BA%8C%E9%98%B6%E5%81%8F%E5%AF%BC%E6%95%B01%EF%BC%89z%3Dx%5E4%2B3%2Ax%5E2%2Ay%2By%5E32%EF%BC%89z%3Dxln%28x%2By%29)
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)
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^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^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)
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
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/ͦ...
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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
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zx=4x^3+6*xy
zy=3*x^2+3y^2
(2)
zx=ln(x+y)+x/(x+y)
zy=x/(x+y)