derivative (2x+6)/(x+9)

解

導関数

\frac{2 x + 6}{x + 9}

\frac{12}{( x + 9 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 x + 6}{x + 9})

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 + 6 ) ( x + 9 ) - \frac{d}{d x} ( x + 9 ) ( 2 x + 6 )}{( x + 9 ) ^{2}}

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

\frac{d}{d x} (x + 9) = 1

= \frac{2 ( x + 9 ) - 1 \cdot ( 2 x + 6 )}{( x + 9 ) ^{2}}

簡素化

\frac{2 ( x + 9 ) - 1 \cdot ( 2 x + 6 )}{( x + 9 ) ^{2}} : \frac{12}{( x + 9 ) ^{2}}

= \frac{12}{( x + 9 ) ^{2}}