If I know $a^1(c)$, $a^2(c)$, and $a^3(c)$, and that
$a(c) = min \left[ a^1(c^1)+a^2(c^2)+a^3(c^3)\right]$
subject to
$c^1+c^2+c^3=c$
can I write an expression for $\frac{da}{dc}$?
Follow-up: Is the solution simpler if we are dealing with convex functions?
This question is related to this one.
Thanks