derivative g(x)=(1-3x)/(5+x)

解

導関数

g (x) = \frac{1 - 3 x}{5 + x}

- \frac{16}{( 5 + x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{1 - 3 x}{5 + 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} ( 1 - 3 x ) ( 5 + x ) - \frac{d}{d x} ( 5 + x ) ( 1 - 3 x )}{( 5 + x ) ^{2}}

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

\frac{d}{d x} (5 + x) = 1

= \frac{( - 3 ) ( 5 + x ) - 1 \cdot ( 1 - 3 x )}{( 5 + x ) ^{2}}

簡素化

\frac{( - 3 ) ( 5 + x ) - 1 \cdot ( 1 - 3 x )}{( 5 + x ) ^{2}} : - \frac{16}{( 5 + x ) ^{2}}

= - \frac{16}{( 5 + x ) ^{2}}