Question

4、求z=(3x的2次方+y的2次方)的(4x-2y)的偏导数。请高人相助。谢谢

Answer 1

Z=(3x^2+y^2)/(4x-2y)
Zx'=[(3x^2+y^2)'(4x-2y)-(4x-2y)'(3x^2+y^2)]/(4x-2y)^2
此处(3x^2+y^2)'大隐芦携野，(4x-2y)'均是对x求导
=(6x(4x-2y)-4(3x^2+y^2)]/(4x-2y)^2
=(12x^2-12xy-4y^2)/(4x-2y)^2
=(3x^2-3xy-y^2)/滚带(2x-y)^2
Zy'=[(3x^2+y^2)'(4x-2y)-(4x-2y)'(3x^2+y^2)]/(4x-2y)^2
此处(3x^2+y^2)'，(4x-2y)'均是对y求导
=(2y(4x-2y)+2(3x^2+y^2)]/(4x-2y)^2
=(6x^2+8xy-2y^2)/(4x-2y)^2
=(3x^2+4xy-y^2)/[2(2x-y)^2]

Answer 2

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