Step-by-step explanation:
Given:
[tex]z = x^4 - 3xy + 4y^3[/tex]
[tex]\dfrac{\partial z}{\partial x} = 4x^3 - 3y \Rightarrow \dfrac{\partial^2z}{\partial x^2} = 12x^2[/tex]
[tex]\dfrac{\partial z}{\partial y} = -3x + 12y^2 \Rightarrow \dfrac{\partial^2z}{\partial x \partial y} = -3[/tex]
[tex]\dfrac{\partial^2z}{\partial y^2} = 24y[/tex]
[tex]\dfrac{\partial^2z}{\partial y \partial x} = -3[/tex]
