derivative of (sqrt(x)/(2x-7))

解

\frac{d}{d x} (\frac{x}{2 x - 7})

\frac{- 2 x - 7}{2 x ( 2 x - 7 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{2 x - 7})

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 x - 7 ) - \frac{d}{d x} ( 2 x - 7 ) x}{( 2 x - 7 ) ^{2}}

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

\frac{d}{d x} (2 x - 7) = 2

= \frac{\frac{1}{2 x} ( 2 x - 7 ) - 2 x}{( 2 x - 7 ) ^{2}}

簡素化

\frac{\frac{1}{2 x} ( 2 x - 7 ) - 2 x}{( 2 x - 7 ) ^{2}} : \frac{- 2 x - 7}{2 x ( 2 x - 7 ) ^{2}}

= \frac{- 2 x - 7}{2 x ( 2 x - 7 ) ^{2}}