问题
若函数 $\textcolor{Orange}{f(x)}$ 在区间 $[a, b]$ 上连续，函数 $\textcolor{Orange}{\phi(x)}$ 在区间 $[a, b]$ 上可导，且变上限积分 $\textcolor{Orange}{F(x)}$ $\textcolor{Orange}{=}$ $\textcolor{Orange}{\int_{a}^{\phi(x)}}$ $\textcolor{Orange}{f(t)}$ $\textcolor{Orange}{\mathrm{d} t}$, 则 $\textcolor{Orange}{F^{\prime}(x)}$ $=$ $?$选项
[A]. $F^{\prime}(x)$ $=$ $f[\phi(x)]$ $\cdot$ $\phi^{\prime}(x)$[B]. $F^{\prime}(x)$ $=$ $f [ \phi(x)]$ $\cdot$ $\phi(x)$
[C]. $F^{\prime}(x)$ $=$ $f[\phi(x)]$
[D]. $F^{\prime}(x)$ $=$ $f[\phi ^{\prime} (x)]$ $\cdot$ $\phi(x)$
$$\textcolor{Orange}{F^{\prime}(x)} =$$ $$\Bigg[ \int_{\textcolor{Yellow}{a}}^{\textcolor{Yellow}{\phi(x)}} \textcolor{Red}{f(t)} \mathrm{d} t \Bigg] \textcolor{Yellow}{^{\prime}} =$$ $$f[\textcolor{Red}{\phi(x)}] \cdot \textcolor{Red}{\phi} \textcolor{Yellow}{^{\prime}} \textcolor{Red}{(x)}.$$