$${\displaystyle {\frac {{\rm d}}{{\rm d}x}}\left(\int _{a}^{b}f(x,x')\,{\rm d}x'\right)=\int _{a}^{b}{\frac {\partial }{\partial x}}f(x,x')\,{\rm d}x'.}$$
• @HaaranAjgaonkar It means that you are integrating w.r.t $x'$, but taking the derivative w.r.t $x$, so the rule above applies – caverac Dec 27 '18 at 12:40