You can use AnalyticCurve to draw curve directly.
Since you used
double u = _view.waveFunction.evaluate(x,t);
to evaluate it's value in your code.
You can calculate u2=_view.waveFunction.evaluate(x,t-ddt);
And you can get du/dt with [u]u2-u/ddt[/u] if [u]ddt[/u] is small enough!
Just calculated it by definition!