derivative (x^2-6x+12)/(x-4)

解

導関数

\frac{x ^{2} - 6 x + 12}{x - 4}

\frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2} - 6 x + 12}{x - 4})

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 + 12 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x ^{2} - 6 x + 12 )}{( x - 4 ) ^{2}}

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

\frac{d}{d x} (x - 4) = 1

= \frac{( 2 x - 6 ) ( x - 4 ) - 1 \cdot ( x ^{2} - 6 x + 12 )}{( x - 4 ) ^{2}}

簡素化

\frac{( 2 x - 6 ) ( x - 4 ) - 1 \cdot ( x ^{2} - 6 x + 12 )}{( x - 4 ) ^{2}} : \frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}

= \frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}