# Small question about derivative

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 $e\in L(0,1)$

Please help me

Thank you

-
add comment

## 1 Answer

You can commute the derivative and the integral operators in this case. See here.

-
$\frac{d}{dt}(\int_0^1 G(t,s)e(s) ds)=\int_0^1 \frac{\partial G(t,s)}{dt} e(s)ds$ it's right ? –  Vrouvrou May 16 at 7:20
yes, you are correct –  julian fernandez May 16 at 7:39
add comment