Question

Is it possible to create a C program that solves derivatives? if so, how?

Answer 1

It's definitely possible.

A good place to start is to create a data type for polynomials.
You could store the factor for each power in an array if you're only dealing with one variable.
So 3x^2 + 4x +5 would be stored as:
{3,4,5} or {5,4,3}

Do this, then evaluate a few derivatives the same way you'd do on paper. Try to see if you can find a general approach that you can apply to polynomials in this form. There is a fairly simple way of doing this for derivatives on polynomials of this form.

If you need to deal with multiple variables, it can get more complex, but you should try to do it with one variable first.

Answer 2

it sounds complex right now...