1. The problem statement, all variables and given/known data A mapping f from an open subset S of Rn into Rm is called smooth if it has continuous partial derivatives of all orders. However, when the domain S is not open one cannot usually speak of partial derivatives. Why? 2. Relevant equations 3. The attempt at a solution In the 1 dimensional case there are not partial derivatives and we can consider the derivative of a function on a closed set by just using the derivative from the left if we are at the left boundary point of the interval. In 2 dimensions I tried creating a counter example, but no luck yet. In the definition of the partial derivative we already assume the domain to be open.