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