$f\in C^{1}[0,\infty)$, $f(0)=0$ and 
$$
f(x)+f'(x)-\frac{1}{x+1}\int\_{0}^{x}f(t)dt=0
$$
then $f'(x)=$ ?

I'v tried in the following ways. First, let $F(x)=\int\_{0}^{x}f(t)dt$, then we are left to solve a second order ODE with initial condition $F(0)=0$, and $F'(0)=0$, but the problem is it seems to me that it's not that easy to solve it.

I hope there are some other ways to handle it that a one year students can understand. (I have tried to write $g(x)=f(x)e^x$ to rewrite the equation, but it doesn't make it easier)