何度も解いて体で覚えましょう!
次の x の関数の導関数を求めよ。
\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*}
【解答】
\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*}
この問題へのリンクはこちら(右クリックで保存)
\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*}
【解答】
\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*}
この問題へのリンクはこちら(右クリックで保存)
\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*}
【解答】
\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*}
この問題へのリンクはこちら(右クリックで保存)
\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*}
【解答】
\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*}
この問題へのリンクはこちら(右クリックで保存)