derivative ((1-x))/((x+2))

解

導関数

\frac{( 1 - x )}{( x + 2 )}

- \frac{3}{( x + 2 ) ^{2}}

解答ステップ

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

商の法則を適用:

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

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

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

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

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

簡素化

\frac{( - 1 ) ( x + 2 ) - 1 \cdot ( 1 - x )}{( x + 2 ) ^{2}} : - \frac{3}{( x + 2 ) ^{2}}

= - \frac{3}{( x + 2 ) ^{2}}