(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A mapping f from an open subset S of R^{n}into R^{m}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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Partial derivatives

**Physics Forums | Science Articles, Homework Help, Discussion**