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

Find the value of $(f g h)^{\prime}(0)$.
Solution: 16 By the product rule, $(f g h)^{\prime}=f^{\prime} g h+f g^{\prime} h+f g h^{\prime}=\left((f g)^{\prime} h+(g h)^{\prime} f+\right.$ $\left.(h f)^{\prime} g\right) / 2$. Evaluated at 0 , this gives 16 .