derivative m(x)=(-x^2+6x-8)/(-x^2+6x-2)

解

導関数

f (x) = \frac{- x ^{2} + 6 x - 8}{- x ^{2} + 6 x - 2}

\frac{- 12 x + 36}{( - x ^{2} + 6 x - 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{- x ^{2} + 6 x - 8}{- x ^{2} + 6 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 ^{2} + 6 x - 8 ) ( - x ^{2} + 6 x - 2 ) - \frac{d}{d x} ( - x ^{2} + 6 x - 2 ) ( - x ^{2} + 6 x - 8 )}{( - x ^{2} + 6 x - 2 ) ^{2}}

\frac{d}{d x} (- x^{2} + 6 x - 8) = - 2 x + 6

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

= \frac{( - 2 x + 6 ) ( - x ^{2} + 6 x - 2 ) - ( - 2 x + 6 ) ( - x ^{2} + 6 x - 8 )}{( - x ^{2} + 6 x - 2 ) ^{2}}

拡張

(- 2 x + 6) (- x^{2} + 6 x - 2) - (- 2 x + 6) (- x^{2} + 6 x - 8) : - 12 x + 36

= \frac{- 12 x + 36}{( - x ^{2} + 6 x - 2 ) ^{2}}