derivative of (2x-1^{-2})

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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