Original Message (ID '324680') By devil: 
In Response To 'Re: Re: Re: derivative of amplitudefrequency c...'

Yes, you are right.
I get the same output.
ampl = 2 \[Pi] Abs[f/(1000 + 2 I f \[Pi])]
and the derivation of it is the same you said
2 \[Pi] (((2 I f \[Pi])/(1000 + 2 I f \[Pi])^2) + 1/(
1000 + 2 I f \[Pi])) Derivative[1][Abs][f/(1000 + 2 I f \[Pi])]
I figure out that ampl is a real function. Im[ampl] is 0!
So thats why Mathematica have no problem to plot it.
The derivation is in addition imaginary ... so Mathematica don't know how to plot. Like you said.
But I can't explain why the derivation of a function should not exist, when I can plot the original function. There are no bounds in my plot.
LogLogPlot[ampl, {f, 0.0000001, 10000000}]
And that's why I think the derivation should exist.
Could the problem are the bounce by f=0 ?
Plot[ampl, {f, 100, 100}]
How can I limit the derivation from 0 to inf so that there are no more bounces?
Could this be the reason why Mathematica can't solve the derivation ? 
