设z=(sinx)^3+y^3-3xy^2,求二阶偏导数,急求,在线等.(请含过程)
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![设z=(sinx)^3+y^3-3xy^2,求二阶偏导数,急求,在线等.(请含过程)](/uploads/image/z/8330183-71-3.jpg?t=%E8%AE%BEz%3D%EF%BC%88sinx%EF%BC%89%5E3%2By%5E3-3xy%5E2%2C%E6%B1%82%E4%BA%8C%E9%98%B6%E5%81%8F%E5%AF%BC%E6%95%B0%2C%E6%80%A5%E6%B1%82%2C%E5%9C%A8%E7%BA%BF%E7%AD%89.%EF%BC%88%E8%AF%B7%E5%90%AB%E8%BF%87%E7%A8%8B%EF%BC%89)
设z=(sinx)^3+y^3-3xy^2,求二阶偏导数,急求,在线等.(请含过程)
设z=(sinx)^3+y^3-3xy^2,求二阶偏导数,急求,在线等.(请含过程)
设z=(sinx)^3+y^3-3xy^2,求二阶偏导数,急求,在线等.(请含过程)
z=(sinx)^3+y^3-3xy^2
dz/dx=3(sinx)^2*cosx-3y^2
dz/dy=3y^2-6xy
d^2z/dx^2=d(dz/dx)/dx=d[3(sinx)^2*cosx-3y^2]/dx=6sinx*(cosx)^2-3(sinx)^3
d^2z/dx^2=d(dz/dy)/dy=d(3y^2-6xy)/dx=6y-6x
d^2z/dxdy=d(dz/dy)/dx=d(dz/dx)/dy=-6y
∂z/∂x = 3 sin²x cosx - 3y² (把 y 视为常数 )
∂²z/∂x² = 3 * 2sinx cosx * cosx - 3 sin³x = 6sinx co²sx - 3 sin³x
∂²z/W...
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∂z/∂x = 3 sin²x cosx - 3y² (把 y 视为常数 )
∂²z/∂x² = 3 * 2sinx cosx * cosx - 3 sin³x = 6sinx co²sx - 3 sin³x
∂²z/∂x∂y = - 6y
∂z/∂y = 3y² - 6xy (把 x 视为常数 )
∂²z/∂y = 6y - 6x
∂²z/∂y∂x = -6y
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dz/dx=3cosx(sinx)^2+3y^3, d2z/dx2=3sinx(cos^2 x-sin^2 x)=3sinxcos2x
dz/dy=3y^2-6xy, d2z/dy2=6y-6x=6(x-y)