Question

Листик с решением скиньте пжл.

Answer 1

$z=x^2y^2-x^4-y^4+2x^2y^3\\dz= frac{partial z}{partial x}, dx+ frac{partial z}{partial y}, dy\\\frac{partial z}{partial x} =2xy^2-4x^3+4xy^3\\ frac{partial z}{partial y} =2x^2y-4y^3+6x^2y^2\\dz=(2xy^2-4x^3+4xy^3)dx+(2x^2y-4y^3+6x^2y^2)dy\\\d^2z=frac{partial ^2z}{partial x^2}, dx^2+2, frac{partial ^2z}{partial xpartial y}, dx, dy+frac{partial ^2z}{partial y^2}, dy^2\\ frac{partial ^2z}{partial x^2}=2y^2-12x^2+4y^3\\ frac{partial ^2z}{partial xpartial y}=4xy+12xy^2$

$frac{partial ^2z}{partial y^2}=2x^2-12y^2+12x^2y\\d^2z=(2y^2-12x^2+4y^3)dx^2+(4xy+12xy^2), dx, dy+\\+(2x^2-12y^2+12x^2y), dy^2$