How can I put a derivitive finding program into this code?

This is (technically) my first post here - bare with me, please. But I wanted to share a piece of code that I created myself! This is for TI-84 calculators to get the greatest common factor between any two functions/numbers, get the roots of any nth degree polynomial, and get the critical/inflection points of any composite function. This function only uses if statements as well!

Here is the code: (note that Z and S were set to be the derivatives of f and g; you have to find these yourself. Set z and s to 1 to use it to find GCF or roots!) (Also, Y1 is found in vars, if you tab right after clicking vars button, pressing enter, then enter again)

To start, put the function/s that you are working with into Y1, Y2, etc...

enter code here :Prompt F,G`:Prompt Z:Prompt S:If Y1=F:If Y2=G:F*G=FS+GZ->H :If X≥Y:X-Y=I->I:Disp I:If I=0:If I>0:Repeat X-Y=J->J:Disp J

That's it! Super simple, but so helpful! But you will see one problem - the function still asks for the derivative of each function instead of having a program built in that does it automatically. I was wondering if anyone has already made a code that does such a thing. If not, how would I start? I am willing to take ideas, build a shell, and debug it!

Thanks so much, and have fun with the code! -Evan