derivative of ((3x-4/(5x+2))^{-5})

解

\frac{d}{d x} ((\frac{3 x - 4}{5 x + 2})^{- 5})

- \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

解答ステップ

\frac{d}{d x} ((\frac{3 x - 4}{5 x + 2})^{- 5})

連鎖法則を適用:

- \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \frac{d}{d x} (\frac{3 x - 4}{5 x + 2})

= - \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \frac{d}{d x} (\frac{3 x - 4}{5 x + 2})

\frac{d}{d x} (\frac{3 x - 4}{5 x + 2}) = \frac{26}{( 5 x + 2 ) ^{2}}

= - \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \cdot \frac{26}{( 5 x + 2 ) ^{2}}

簡素化

- \frac{5}{( \frac{3 x - 4}{5 x + 2} ) ^{6}} \cdot \frac{26}{( 5 x + 2 ) ^{2}} : - \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}

= - \frac{130 ( 5 x + 2 ) ^{4}}{( 3 x - 4 ) ^{6}}