derivative ((x^2-1))/(2x-3)

解

導関数

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

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

解答ステップ

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

商の法則を適用:

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

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

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

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

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

拡張

2 x (2 x - 3) - 2 (x^{2} - 1) : 2 x^{2} - 6 x + 2

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