derivative of (4x/(7x-2))

解

\frac{d}{d x} (\frac{4 x}{7 x - 2})

- \frac{8}{( 7 x - 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{4 x}{7 x - 2})

定数を除去:

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

= 4 \frac{d}{d x} (\frac{x}{7 x - 2})

商の法則を適用:

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

= 4 \cdot \frac{\frac{d x}{d x} ( 7 x - 2 ) - \frac{d}{d x} ( 7 x - 2 ) x}{( 7 x - 2 ) ^{2}}

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

\frac{d}{d x} (7 x - 2) = 7

= 4 \cdot \frac{1 \cdot ( 7 x - 2 ) - 7 x}{( 7 x - 2 ) ^{2}}

簡素化

4 \cdot \frac{1 \cdot ( 7 x - 2 ) - 7 x}{( 7 x - 2 ) ^{2}} : - \frac{8}{( 7 x - 2 ) ^{2}}

= - \frac{8}{( 7 x - 2 ) ^{2}}