Answer
$$ (f g h)^{\prime} =f^{\prime} g h+f g^{\prime} h+f g h^{\prime}$$
Work Step by Step
Since
\begin{align*}
(f g h)^{\prime}&=f(gh)'+f'(gh) \\
&=f\left(g h^{\prime}+h g^{\prime}\right)+g h f^{\prime}\\
&=f^{\prime} g h+f g^{\prime} h+f g h^{\prime}
\end{align*}
Then $$ (f g h)^{\prime} =f^{\prime} g h+f g^{\prime} h+f g h^{\prime}$$
