The Mudcat Café TM
Thread #59418   Message #3114694
Posted By: Rapparee
15-Mar-11 - 11:34 PM
Thread Name: BS: The Mother of all BS threads
Subject: RE: BS: The Mother of all BS threads
If ƒ is a real-valued function on Rn, then the partial derivatives of ƒ measure its variation in the direction of the coordinate axes. For example, if ƒ is a function of x and y, then its partial derivatives measure the variation in ƒ in the x direction and the y direction. They do not, however, directly measure the variation of ƒ in any other direction, such as along the diagonal line y = x.

A whirling derivative would also be scalar, as it would have to satisfy velocity as well as direction. A three- or more dimensional model is likely needed, especially if the whirling derivative were to vector linearly as well as rotationally.