導関数の基本式I（微分の公式I）

導関数の基本式 I（微分の公式I）

• ${\left\{c\right\}}^{\prime }=0$

すなわち

$f\left(x\right)=c\to {f}^{\prime }\left(x\right)=0$     導出計算

• ${\left\{cg\left(x\right)\right\}}^{\prime }=c{g}^{\prime }\left(x\right)$

すなわち

$f\left(x\right)=cg \left(x\right)\to {f}^{\prime }\left(x\right)=c{g}^{\prime }\left(x\right)$     導出計算

• ${\left\{g\left(x\right)±h\left(x\right)\right\}}^{\prime }={g}^{\prime }\left(x\right)±{h}^{\prime }\left(x\right)$

すなわち

$f\left(x\right)=g\left(x\right)±h\left(x\right)$ $\to {f}^{\prime }\left(x\right)={g}^{\prime }\left(x\right)±{h}^{\prime }\left(x\right)$     導出計算

• ${\left\{g\left(x\right)h\left(x\right)\right\}}^{\prime }$$={g}^{\prime }\left(x\right)h\left(x\right)+g\left(x\right){h}^{\prime }\left(x\right)$

すなわち

$f\left(x\right)=g\left(x\right)h\left(x\right)$ $\to {f}^{\prime }\left(x\right)={g}^{\prime }\left(x\right)h\left(x\right)+g\left(x\right)h{\left(x\right)}^{\prime }$     導出計算

• ${\left\{\frac{1}{g\left(x\right)}\right\}}^{\prime }=-\frac{{g}^{\prime }\left(x\right)}{{\left\{g\left(x\right)\right\}}^{2}}$

すなわち

$f\left(x\right)=\frac{1}{g\left(x\right)}\to {f}^{\prime }\left(x\right)=-\frac{{g}^{\prime }\left(x\right)}{{\left\{g\left(x\right)\right\}}^{2}}$       導出計算

• ${\left\{\frac{h\left(x\right)}{g\left(x\right)}\right\}}^{\prime }=\frac{{h}^{\prime }\left(x\right)g\left(x\right)-h\left(x\right){g}^{\prime }\left(x\right)}{{\left\{g\left(x\right)\right\}}^{2}}$

すなわち

$f\left(x\right)=\frac{h\left(x\right)}{g \left(x\right)}$ $\to {f}^{\prime }\left(x\right)=\frac{{h}^{\prime }\left(x\right)g\left(x\right)-h\left(x\right){g}^{\prime }\left(x\right)}{{\left\{g\left(x\right)\right\}}^{2}}$     導出計算

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