derivative G(t)=(1-4t)/(5+t)

解

導関数

G (t) = \frac{1 - 4 t}{5 + t}

- \frac{21}{( 5 + t ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{1 - 4 t}{5 + t})

商の法則を適用:

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

= \frac{\frac{d}{d t} ( 1 - 4 t ) ( 5 + t ) - \frac{d}{d t} ( 5 + t ) ( 1 - 4 t )}{( 5 + t ) ^{2}}

\frac{d}{d t} (1 - 4 t) = - 4

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

= \frac{( - 4 ) ( 5 + t ) - 1 \cdot ( 1 - 4 t )}{( 5 + t ) ^{2}}

簡素化

\frac{( - 4 ) ( 5 + t ) - 1 \cdot ( 1 - 4 t )}{( 5 + t ) ^{2}} : - \frac{21}{( 5 + t ) ^{2}}

= - \frac{21}{( 5 + t ) ^{2}}