The recursive parser thing is definitely the best way to go about the symbolic differentiator. An initial expansion simulates the sum and product rules (along with rules for sin, cos, natural logs, etc.), while the recursive nature simulates the chain rule.

Now, if you really want to blow your mind, write a symbolic integator I''ll let you off and assume the starting condition is (0,0). Muhaha!

Good luck. If anything, this should be a fun and educational endeavor.

hmmm, maybe I shoud just do it numerically. Any idea on how professinal calcualtors go?

Numerically, you basically use the formulas given in the above posts. Remember, the derivative describes the rate of change, so it''s really the difference in y values over the difference in x values (slope), as the distance between those two x values approaches zero. So use a really small number instead of zero for how far apart they are So if you wanted to find the derivative at f(5), then take a really small interval (h), like 0.05, and find the slope between two points on either side of f(5):

f(5.05) - f(4.95)-----------------      0.10

This is basically what AP said before about the midpoint rule.

thanks zipster. I didn''t mean how they did numerical differintiation, my question was which method did pro calcualtors use?

More advanced calculators such as the TI-89 probably use something similar to what''s been described here already. I don''t know how complex a function they can integrate, but they do pretty well for most.

Folks,

Lets keep this thread on topic. laeuchli asked for a link to an article, not a discussion. Since no mention was given of game development or a work/development in progress, I''d prefer that any further posts to this thread be a link to the requested article, nothing more.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.