A Tiny (WP34S) program does a lot

[BarryMead]

I am VERY IMPRESSED with how much "behind the scenes" computation power is going on with these
simple looking WP-34S functions. Essentially the calculator sets up a double nested loop submitting
intelligent guesses to the outer function, which calls an inner loop to compute the first derivative of the guesses.

The result is empowering, even though I did not know what the derivative (DiGamma X+1) of the Factorial function (Gamma of X+1) was, the calculator was able to figure it out with it's intelligent internal looping. Even though I chose
a bad example for a function with no algebraically defined derivative, there must be functions with no known derivative to which this concept could be applied.

Thanks for your informative replies. I learn something new every day.