An example is an example, an example is not general. I gave erf because it did not work in general using the general method. The reason why erf works is PRECISELY because it is defined by an integeral of a gaussian so the derivative simply returns a gaussian AND then the fourier transform of a gaussian is a gaussian.
For functions that are not defined by an integeral, the derivative wont necessarily simplify it in to somethign that has a fourier transform. You want a specific case as if that is a general solution.
For something to be general means that it works for all inputs. What happens when I want to try a different function? Your method fails, you come up with a new one. I try it, it works, then I try a new function and your method fails... and the process is not general.
It is not about calculating a derivative symbolically, it is about taking the inverse transform of a function in general... seems you fail to understand that.
Your method works ONLY because of the special nature of erf. It does not work in general. How many functions do I have to show you to prove that? And how many will it take for you to realize that?
You want a function? Zeta(s), happy? Now try your derivative method!
Oh, maybe you figured out a trick with Zeta(s)? What about Zeta(s*Zeta(s + 1))? Oh, another trick? What about Zeta(s*cos(Zeta(s + erf(s^2 -sin(Zeta(s)))))*Zeta(s^2)^3. Ok, you found a trick! Great, you are now famous!
To plot something does not require symbolic manipulation. I realize maple is a CAS, but plotting functions should be possible and easy, even transforms of functions. Plotting helps visualize functions and it is an important area of mathematics. To limit plotting of functions to only those that are symbolically computable is nonsense.