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Find the four second partial derivatives. Observe that the second mixed partials are equal.

Find The Four Second Partial Derivatives Observe That The Second Mixed Partials Are Equal class=

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Trancescientidn

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]

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