Hey, I need help with the following total differential

In principle, I need to differentiate H wrt $\displaystyle q_0$, $\displaystyle t_{WA_c}$, $\displaystyle t_{A_cA}$, and $\displaystyle t_{EC}$. The problem are the differentials wrt $\displaystyle t_{WA_c}$ and $\displaystyle t_{EC}$. I cannot substitute c(s) simply.

$\displaystyle H \equiv q_0 - \int_{t_{WA_c}}^{t_{A_cA}} \psi(s) \frac{1-\Psi(c(s))}{1-\Psi(s)} ds$

s.t. $\displaystyle c(s)= t_{EC} + \int_{t_{WA_c}}^{s} \frac{1-\Psi(t)}{2} \frac{\phi(t)}{\phi(c(t))} dt$