derivative of ((-4x(2x-2))/(-3x^2+1))

解

\frac{d}{d x} (\frac{( - 4 x ) ( 2 x - 2 )}{- 3 x ^{2} + 1})

- \frac{4 ( - 6 x ^{2} + 4 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{( - 4 x ) ( 2 x - 2 )}{- 3 x ^{2} + 1})

簡素化

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

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

定数を除去:

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

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

商の法則を適用:

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

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

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

\frac{d}{d x} (- 3 x^{2} + 1) = - 6 x

= - 4 \cdot \frac{( 4 x - 2 ) ( - 3 x ^{2} + 1 ) - ( - 6 x ) x ( 2 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}

簡素化

- 4 \cdot \frac{( 4 x - 2 ) ( - 3 x ^{2} + 1 ) - ( - 6 x ) x ( 2 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}} : - \frac{4 ( - 6 x ^{2} + 4 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}

= - \frac{4 ( - 6 x ^{2} + 4 x - 2 )}{( - 3 x ^{2} + 1 ) ^{2}}