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

asked Feb 16, 2023 175k views

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Explanation:

Given:

z = x^4 - 3xy + 4y^3

$(\partial z)/(\partial x) = 4x^3 - 3y \Rightarrow (\partial^2z)/(\partial x^2) = 12x^2$

$(\partial z)/(\partial y) = -3x + 12y^2 \Rightarrow (\partial^2z)/(\partial x \partial y) = -3$

$(\partial^2z)/(\partial y^2) = 24y$

$(\partial^2z)/(\partial y \partial x) = -3$

Tura answered Feb 23, 2023

by Tura

6.2k points

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