Well, the major difference here is that your C method requires that all this stuff be defined at compile time, while the Scheme deriv works with even functions

Well, the major difference here is that your C method requires that all this stuff be defined at compile time, while the Scheme deriv works with even functions that are dynamically defined at run time, anonymous functions, etc. I'm not sure how you would do that in C, other than by Greenspunning up an implementation of first-class functions.