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

解

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

\frac{- x + 6}{2 ( 2 - x ) 2 - x}

解答ステップ

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

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

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

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

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

簡素化

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

= \frac{- x + 6}{2 ( 2 - x ) 2 - x}