derivative t/((t-3)^2)

解

導関数

\frac{t}{( t - 3 ) ^{2}}

\frac{- 3 - t}{( t - 3 ) ^{3}}

解答ステップ

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

商の法則を適用:

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

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

\frac{d t}{d t} = 1

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

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

簡素化

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

= \frac{- 3 - t}{( t - 3 ) ^{3}}