derivative (-3x+12)/(2sqrt(6-x))

解

導関数

\frac{- 3 x + 12}{2 6 - x}

\frac{3 x - 24}{4 ( 6 - x ) 6 - x}

解答ステップ

\frac{d}{d x} (\frac{- 3 x + 12}{2 6 - x})

定数を除去:

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

= \frac{1}{2} \frac{d}{d x} (\frac{- 3 x + 12}{6 - x})

商の法則を適用:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( - 3 x + 12 ) 6 - x - \frac{d}{d x} ( 6 - x ) ( - 3 x + 12 )}{( 6 - x ) ^{2}}

\frac{d}{d x} (- 3 x + 12) = - 3

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

= \frac{1}{2} \cdot \frac{( - 3 ) 6 - x - ( - \frac{1}{2 6 - x} ) ( - 3 x + 12 )}{( 6 - x ) ^{2}}

簡素化

\frac{1}{2} \cdot \frac{( - 3 ) 6 - x - ( - \frac{1}{2 6 - x} ) ( - 3 x + 12 )}{( 6 - x ) ^{2}} : \frac{3 x - 24}{4 ( 6 - x ) 6 - x}

= \frac{3 x - 24}{4 ( 6 - x ) 6 - x}