derivative (1-3t)/(6+t)

解

導関数

\frac{1 - 3 t}{6 + t}

- \frac{19}{( 6 + t ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{1 - 3 t}{6 + 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 - 3 t ) ( 6 + t ) - \frac{d}{d t} ( 6 + t ) ( 1 - 3 t )}{( 6 + t ) ^{2}}

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

\frac{d}{d t} (6 + t) = 1

= \frac{( - 3 ) ( 6 + t ) - 1 \cdot ( 1 - 3 t )}{( 6 + t ) ^{2}}

簡素化

\frac{( - 3 ) ( 6 + t ) - 1 \cdot ( 1 - 3 t )}{( 6 + t ) ^{2}} : - \frac{19}{( 6 + t ) ^{2}}

= - \frac{19}{( 6 + t ) ^{2}}