derivative of (94x/(99x-94))

解

\frac{d}{d x} (\frac{94 x}{99 x - 94})

- \frac{8836}{( 99 x - 94 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{94 x}{99 x - 94})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 94 \frac{d}{d x} (\frac{x}{99 x - 94})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 94 \cdot \frac{\frac{d x}{d x} ( 99 x - 94 ) - \frac{d}{d x} ( 99 x - 94 ) x}{( 99 x - 94 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (99 x - 94) = 99

= 94 \cdot \frac{1 \cdot ( 99 x - 94 ) - 99 x}{( 99 x - 94 ) ^{2}}

簡素化

94 \cdot \frac{1 \cdot ( 99 x - 94 ) - 99 x}{( 99 x - 94 ) ^{2}} : - \frac{8836}{( 99 x - 94 ) ^{2}}

= - \frac{8836}{( 99 x - 94 ) ^{2}}