derivative (sqrt(x))/(6x-6)

解

導関数

\frac{x}{6 x - 6}

- \frac{x + 1}{12 x ( x - 1 ) ^{2}}

解答ステップ

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

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

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

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

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

簡素化

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

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