derivative of (2x/(-8x-1))

解

\frac{d}{d x} (\frac{2 x}{- 8 x - 1})

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

解答ステップ

\frac{d}{d x} (\frac{2 x}{- 8 x - 1})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{- 8 x - 1})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d x}{d x} ( - 8 x - 1 ) - \frac{d}{d x} ( - 8 x - 1 ) x}{( - 8 x - 1 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (- 8 x - 1) = - 8

= 2 \cdot \frac{1 \cdot ( - 8 x - 1 ) - ( - 8 ) x}{( - 8 x - 1 ) ^{2}}

簡素化

2 \cdot \frac{1 \cdot ( - 8 x - 1 ) - ( - 8 ) x}{( - 8 x - 1 ) ^{2}} : - \frac{2}{( - 8 x - 1 ) ^{2}}

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