derivative ((x+1)(x+2))/((x-1)(x-2))

解

導関数

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

\frac{- 6 x ^{2} + 12}{( x - 1 ) ^{2} ( x - 2 ) ^{2}}

解答ステップ

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

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

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

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

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

簡素化

\frac{( 2 x + 3 ) ( x - 1 ) ( x - 2 ) - ( 2 x - 3 ) ( x + 1 ) ( x + 2 )}{( ( x - 1 ) ( x - 2 ) ) ^{2}} : \frac{- 6 x ^{2} + 12}{( x - 1 ) ^{2} ( x - 2 ) ^{2}}

= \frac{- 6 x ^{2} + 12}{( x - 1 ) ^{2} ( x - 2 ) ^{2}}