Question

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

Answer 1

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`