Листик с решением скиньте пжл.

Решите задачу:

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

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