derivative of (4x-6/(x-6))

解

\frac{d}{d x} (\frac{4 x - 6}{x - 6})

- \frac{18}{( x - 6 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{4 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} ( 4 x - 6 ) ( x - 6 ) - \frac{d}{d x} ( x - 6 ) ( 4 x - 6 )}{( x - 6 ) ^{2}}

\frac{d}{d x} (4 x - 6) = 4

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

= \frac{4 ( x - 6 ) - 1 \cdot ( 4 x - 6 )}{( x - 6 ) ^{2}}

簡素化

\frac{4 ( x - 6 ) - 1 \cdot ( 4 x - 6 )}{( x - 6 ) ^{2}} : - \frac{18}{( x - 6 ) ^{2}}

= - \frac{18}{( x - 6 ) ^{2}}