求函数z=4x^3y^2-5x^2y^4的全微分
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z=4x^3.y^2-5x^2.y^4
dz
=d(4x^3.y^2-5x^2.y^4)
=4(x^3.dy^2 + y^2.dx^3) - 5(x^2.dy^4 +y^4.dx^2)
=4[x^3.(2ydy) + y^2.(3x^2.dx) ] - 5[x^2.(4y^3dy) +y^4.(2xdx) ]
=4(2x^3.ydy + 3x^2.y^2dx ] - 5[4x^2.y^3dy +2xy^4dx ]
dz
=d(4x^3.y^2-5x^2.y^4)
=4(x^3.dy^2 + y^2.dx^3) - 5(x^2.dy^4 +y^4.dx^2)
=4[x^3.(2ydy) + y^2.(3x^2.dx) ] - 5[x^2.(4y^3dy) +y^4.(2xdx) ]
=4(2x^3.ydy + 3x^2.y^2dx ] - 5[4x^2.y^3dy +2xy^4dx ]
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