Suppose $f(u,x)$ is differentiable. In general, how to compute
$\displaystyle{\dfrac{d}{dx}\int_a^xf(u,x)du}$.
I guess the answer should involve $f$ and its partial derivatives, but I have no idea how to do it. This question is inspired by $\displaystyle{\dfrac{d}{dx}\int^x_ag(u)h(x)du}$. In this case, we have $f(u,x)=g(u)h(x)$, so the solution is quite easy.
