Derivative of magnitude function

Hi all,

please refer to attached files (Prime and Mathcad versions).

I have a 3 functions:

1) Ha(s,...) - a filter function (not really important what it is)

2) M(s,...) - magnitude of Ha(s)

3) D(s,...) - derivative of M(s)

When I plot M(s) and D(s) with s replaced with iw, I would expect to see the derivative function have a value of 0 when the magnitude is at turning points but this is not the case.  Can you spot my error?

Thanks,

D.