What is the most efficient way of computing derivative of Riemann zeta function?
If you let Mathematica to plot $\left|\zeta(1/2+i x)\right|$ say on interval $0<x<100$ it is very fast. But if you let it to plot $\left|\zeta'(1/2+i x)\right|$ it takes "ages" to finish. I do not understand why this two things should be of different difficulty (computational complexity).
Any ideas how to implement better algorithm in Mathematica?