Given this expression:
$$\int^{T}_{0} c(t)L(t)exp(\int^T_tr(s)ds)dt$$
how do I take derivative wrt to $T$?
I know that I should be using Fundamental Theorem of Calculus and Chain Rule, but I'm not sure how to apply it.
My attempt:
$$F(T) = \int^{T}_{0} c(t)L(t)exp(\int^T_tr(s)ds)dt$$ Then:
$$F'(T) = c(t)L(t)exp(\int^T_tr(s)ds)r(T)$$