d/(dt)(2/(t^2+2))

解

\frac{d}{d t} (\frac{2}{t ^{2} + 2})

- \frac{4 t}{( t ^{2} + 2 ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{2}{t ^{2} + 2})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

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

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

\frac{d}{d t} (t^{2} + 2) = 2 t

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

簡素化

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

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