Question

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

Answer 1

Step-by-step explanation:

Given:

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

$\dfrac{\partial z}{\partial x} = 4x^3 - 3y \Rightarrow \dfrac{\partial^2z}{\partial x^2} = 12x^2$

$\dfrac{\partial z}{\partial y} = -3x + 12y^2 \Rightarrow \dfrac{\partial^2z}{\partial x \partial y} = -3$

$\dfrac{\partial^2z}{\partial y^2} = 24y$

$\dfrac{\partial^2z}{\partial y \partial x} = -3$