Out= 2*Pi*Abs[f/(1000 + (2*I)*f*Pi)]
Out= 2*Pi*(((-2*I)*f*Pi)/(1000 + (2*I)*f*Pi)^2 + (1000 + (2*I)*f*Pi)^(-1))*Abs'[f/(1000 + 2*I)*f*Pi)]
What do you want the derivative of Abs of a complex value to be? What is Abs'[3/I] for example? When you can decide that then perhaps a function can be found that will provide you Real values for a plot.