Differentials ux and external functions

DEar all,

I haven't found any answer in the external function section of the user's guide for what appears to be a really simple question.

I need to create an external function which will simply compute log(\partial_x u * x).

I noticed that it as possible to create an external function and pass 'x' and 'ux' as arguments to my external function, but I'm just wondering if an external function fun(x,ux) defined like this is legit or not :

function [out]=fun(x,ux)
out = x.*ux;
end

I read that Comsol likes to call this external function a minimal number of times, for computation speed. And so, it usually give sets of values for x, and I guess set of values for ux
However, I can't picture what ux is gonna be in this case... So I'm quite sure my function is not legit.

Just wondering if anybody knows how this works. Or can provide an exemple model implementing such a process.
BR,

M

PS : This example is really simple, I'm not even obliged to create an external function. But for some reasons I'm not detailing here, I absolutely NEED an external function.