How to apply Leibniz rule for this integral? I am struck with the problem of how to evaluate the following integration:
$$\frac{d}{dt}\int_0^{a(t)}{(a (t)-s)^{\alpha-1}f (s) ds}$$
where $f(s)$ is differentiable
and $\alpha\in (0,1)$. The problem is the integrand might not converge when substituting the upper limit

$$\int\limits_{0}^{a(t)}{(a(t)-s)^{\alpha-1}}f(s)ds = \left|-\frac{(a(t)-s)^\alpha}{\alpha}f(s) \right|_{0}^{a(t)}+\frac{1}{\alpha}\int\limits_{0}^{a(t)}{(a(t)-s)^\alpha}{f^{\prime}(s)}ds$$
