derivative (6x-1)/(2x+9)

解

導関数

\frac{6 x - 1}{2 x + 9}

\frac{56}{( 2 x + 9 ) ^{2}}

解答ステップ

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

\frac{d}{d x} (6 x - 1) = 6

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

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

拡張

6 (2 x + 9) - 2 (6 x - 1) : 56

= \frac{56}{( 2 x + 9 ) ^{2}}