derivative f(x)=(3-x)/(x+1)

解

導関数

f (x) = \frac{3 - x}{x + 1}

- \frac{4}{( x + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{3 - x}{x + 1})

商の法則を適用:

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

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

\frac{d}{d x} (3 - x) = - 1

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

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

簡素化

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

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