derivative (1-2t)/(1+3t)

解

導関数

\frac{1 - 2 t}{1 + 3 t}

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

解答ステップ

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

\frac{d}{d t} (1 - 2 t) = - 2

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

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

簡素化

\frac{( - 2 ) ( 1 + 3 t ) - 3 ( 1 - 2 t )}{( 1 + 3 t ) ^{2}} : - \frac{5}{( 1 + 3 t ) ^{2}}

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