We have the function:

defined for:

It is clear that the function is defined for all values of x, y and z that satisfy the conditions above. Moreover it can be verified that it is constant and its value equals pi.

I need to find the total differential of the function (I know it must be null, since the function itself is constant, but I still need to prove this). However, it's just too complicated, differentiating with respect to each variable: the expression is far too hard to handle.

Can anyone come up with a smart substitution that should make the total differential easier to work on, and prove finally that it is 0? Thanks guys.