Question

In what form, typically, is the 2nd derivative of a multivariable function?

Answer 1

The second derivative of a multivariable function is typically represented in matrix form, known as the Hessian matrix. It is a square matrix of second order partial derivatives of the function. If the function f(x,y) has continuous second order partial derivatives, then the Hessian matrix is:

H(f) = | ∂2f/∂x2 ∂2f/∂x∂y |
| ∂2f/∂y∂x ∂2f/∂y2 |