Gradient & Hessian Calculator

A function of several variables. Write products explicitly (x*y) and powers with ^. The gradient collects its first partial derivatives, the Hessian its second ones.

The variables to differentiate with respect to, e.g. x, y. Their order sets the order of the gradient entries and the Hessian rows and columns.

Optional coordinates, one number per variable in the same order. The gradient and Hessian are evaluated there, and the definiteness test classifies the point as minimum, maximum or saddle if the gradient vanishes.