Answer
$$
\begin{aligned} \frac{d}{d x}[f(x) g(x) h(x)] &=\frac{d}{d x}[(f(x) g(x)) h(x)] \\ &=\frac{d}{d x}[f(x) g(x)] h(x)+f(x) g(x) h^{\prime}(x) \\ &=\left[f(x) g^{\prime}(x)+g(x) f^{\prime}(x)\right] h(x)+f(x) g(x) h^{\prime}(x) \\ &=f^{\prime}(x) g(x) h(x)+f(x) g^{\prime}(x) h(x)+f(x) g(x) h^{\prime}(x) \end{aligned}
$$
Work Step by Step
$$
\begin{aligned} \frac{d}{d x}[f(x) g(x) h(x)] &=\frac{d}{d x}[(f(x) g(x)) h(x)] \\ &=\frac{d}{d x}[f(x) g(x)] h(x)+f(x) g(x) h^{\prime}(x) \\ &=\left[f(x) g^{\prime}(x)+g(x) f^{\prime}(x)\right] h(x)+f(x) g(x) h^{\prime}(x) \\ &=f^{\prime}(x) g(x) h(x)+f(x) g^{\prime}(x) h(x)+f(x) g(x) h^{\prime}(x) \end{aligned}
$$
