derivative (2x-5)/(x^2-1)

解

導関数

\frac{2 x - 5}{x ^{2} - 1}

\frac{- 2 x ^{2} + 10 x - 2}{( x ^{2} - 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 x - 5}{x ^{2} - 1})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 2 x - 5 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 2 x - 5 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (2 x - 5) = 2

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

= \frac{2 ( x ^{2} - 1 ) - 2 x ( 2 x - 5 )}{( x ^{2} - 1 ) ^{2}}

拡張

2 (x^{2} - 1) - 2 x (2 x - 5) : - 2 x^{2} + 10 x - 2

= \frac{- 2 x ^{2} + 10 x - 2}{( x ^{2} - 1 ) ^{2}}