Does anyone know any general approach for something like this: $$ \frac{d}{dx}\int_{-\infty}^{x}f(x,u)du\qquad\text{or}\qquad\frac{d}{dx}\int_{x}^{\infty}f(x,u)du\qquad $$
Basically, I'm trying to take the derivative with respect to a parameter when that parameter is both one of the limits of integration and inside the integral itself. Now, I tried applying the FTC to my specific problem and writing $f(x,x)$, but this didn't give me the right results. Any suggestions?
See Differentiation under the integral sign