I have a set of functions f_n that are functions of several variables c_m.
I'd like to give MMa a simple rule like df_n/dc_m = f_(n+m) but have it still use ordinary derivative rules on functions of f_n.
For example, if I ask for the derivative of (f_1 - f_0)^2 wrt c_2, I'd like MMa to apply the power rule (or other calc rules) on its own, but then apply the rule I supplied and return 2(f_1-f_0)(f_3-f_2). If I ask for the derivative of sin(f_123) wrt c_14, I'd like it to return cos(f_123)*f_137. And so on...
I posted my failed code attempts in my first versions of this Question, but those just seemed to confuse commenters as to WHAT I was trying to do. How can I get MMa to do what I want here?