derivative of (3x/(4x-2))

解

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

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

解答ステップ

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

定数を除去:

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

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

商の法則を適用:

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

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

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

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

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

簡素化

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

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