Partial Derivatives: Higher Order and Multi-variables

This lecture covers the concept of higher-order partial derivatives for a function f: E→R, defining a second partial derivative if the function has a partial derivative with respect to another variable. It introduces the notion of f being of class C²(E) if all second partial derivatives are continuous. The lecture also explains the definition of a multi-integer with n variables of order p and how to perform derivations up to order q ≤ p in any order for a function in CP(E).