Derivative of triple product at zero

We are given the values of the differentiable real functions $f$, $g$, $h$, as well as the derivatives of their pairwise products, at $x=0$: $$ f(0)=1 ; \quad g(0)=2 ; \quad h(0)=3 ; \quad (g h)'(0)=4 ; \quad (h f)'(0)=5 ; \quad (f g)'(0)=6 . $$ Find the value of $(f g h)'(0)$.