derivative (1/(1-2x))^3

解

導関数

(\frac{1}{1 - 2 x})^{3}

\frac{6}{( 1 - 2 x ) ^{4}}

解答ステップ

\frac{d}{d x} ((\frac{1}{1 - 2 x})^{3})

連鎖法則を適用:

3 (\frac{1}{1 - 2 x})^{2} \frac{d}{d x} (\frac{1}{1 - 2 x})

= 3 (\frac{1}{1 - 2 x})^{2} \frac{d}{d x} (\frac{1}{1 - 2 x})

\frac{d}{d x} (\frac{1}{1 - 2 x}) = \frac{2}{( 1 - 2 x ) ^{2}}

= 3 (\frac{1}{1 - 2 x})^{2} \frac{2}{( 1 - 2 x ) ^{2}}

簡素化

3 (\frac{1}{1 - 2 x})^{2} \frac{2}{( 1 - 2 x ) ^{2}} : \frac{6}{( 1 - 2 x ) ^{4}}

= \frac{6}{( 1 - 2 x ) ^{4}}