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

解

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

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

解答ステップ

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

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

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

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

簡素化

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

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