derivative of (((-2x-1)/((-4x+2)))^5)

解

\frac{d}{d x} ((\frac{( - 2 x - 1 )}{( - 4 x + 2 )})^{5})

- \frac{5 ( - 2 x - 1 ) ^{4}}{8 ( 2 x - 1 ) ^{6}}

解答ステップ

\frac{d}{d x} ((\frac{( - 2 x - 1 )}{( - 4 x + 2 )})^{5})

連鎖法則を適用:

5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} \frac{d}{d x} (\frac{- 2 x - 1}{- 4 x + 2})

= 5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} \frac{d}{d x} (\frac{- 2 x - 1}{- 4 x + 2})

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

= 5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} (- \frac{2}{( 2 x - 1 ) ^{2}})

簡素化

5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} (- \frac{2}{( 2 x - 1 ) ^{2}}) : - \frac{5 ( - 2 x - 1 ) ^{4}}{8 ( 2 x - 1 ) ^{6}}

= - \frac{5 ( - 2 x - 1 ) ^{4}}{8 ( 2 x - 1 ) ^{6}}