定積分で表された関数を微分する便利な公式とは

\def\Function{(3t^2-2t-1)\,dt}
\def\Moji{x}
\def\Teisu{0}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} & \\
\colMM{green}{\Uarr 定数}　　\colBX{bisque}{$\small \Moji$}\colMM{magenta}{\Uarr 以外の式}
\end{align*}

\def\Function{(3t^2-2t-1)\,dt}
\def\Moji{x}
\def\Teisu{0}
\def\Kotae{3x^2-2x-1}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\colMM{orange}{\Moji で微分} & \colMM{orange}{\Darr}\\
& \colBX{bisque}{$\displaystyle\dfrac{d}{d\Moji}$} \int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} \\
& 　　　　　\colMM{red}{\swarrow } \colBX{bisque}{$\Moji$}\colMM{red}{を代入}\\
&= \Kotae
\end{align*}

\def\Function{7\,dt}
\def\Moji{x}
\def\Teisu{0}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} & \\
\colMM{green}{\Uarr 定数}　&\colBX{bisque}{$\small \Moji$}\colMM{magenta}{\nwarrow 以外の式}
\end{align*}

\def\Function{7\,dt}
\def\Moji{x}
\def\Teisu{0}
\def\Kotae{7}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\colMM{orange}{\Moji で微分} & \colMM{orange}{\Darr}\\
& \colBX{bisque}{$\displaystyle\dfrac{d}{d\Moji}$} \int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} \\
& 　　　\colMM{red}{\swarrow } \colBX{bisque}{$\Moji$}\colMM{red}{を代入 \cdots できないけどね}\\
&= \Kotae
\end{align*}

\def\Function{(2t+3)\,dt}
\def\Moji{x}
\def\Teisu{0}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} & \\
\colMM{green}{\Uarr 定数}　　　\colBX{bisque}{$\small \Moji$} & \colMM{magenta}{\nwarrow 以外の式}
\end{align*}

\def\Function{(2t+3)\,dt}
\def\Moji{x}
\def\Teisu{0}
\def\Kotae{2x+3}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\colMM{orange}{\Moji で微分} & \colMM{orange}{\Darr}\\
& \colBX{bisque}{$\displaystyle\dfrac{d}{d\Moji}$} \int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} \\
& 　　　\colMM{red}{\swarrow } \colBX{bisque}{$\Moji$}\colMM{red}{を代入}\\
&= \Kotae
\end{align*}

\def\Function{(t^2+3t-4)\,dt}
\def\Moji{x}
\def\Teisu{1}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} & \\
\colMM{green}{\Uarr 定数}　　　\colBX{bisque}{$\small \Moji$} & \colMM{magenta}{\nwarrow 以外の式}
\end{align*}

\def\Function{(t^2+3t-4)\,dt}
\def\Moji{x}
\def\Teisu{1}
\def\Kotae{x^2+3x-4}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
\colMM{orange}{\Moji で微分} & \colMM{orange}{\Darr}\\
& \colBX{bisque}{$\displaystyle\dfrac{d}{d\Moji}$} \int_{\colBX{palegreen}{$\scriptsize \Teisu$}}^{\colBX{bisque}{$\small \Moji$}} \colBX{violet}{$\Function$} \\
& 　　　\colMM{red}{\swarrow } \colBX{bisque}{$\Moji$}\colMM{red}{を代入}\\
&= \Kotae
\end{align*}