how to derive $\int_0^1 G(t,s) e(s)ds$ with respect to $t$

Where $G(t,s)$ is a Green function and $e:(0,1)\rightarrow \mathbb{R}$ continuous and $e\in L(0,1)$

$\frac{d}{dt}(\int_0^1 G(t,s)e(s) ds)=\int_0^1 \frac{\partial G(t,s)}{dt} e(s)ds$ it's right ? – Vrouvrou May 16 '13 at 7:20