derivative (8t)/(t^2+9)

解

導関数

\frac{8 t}{t ^{2} + 9}

\frac{8 ( - t ^{2} + 9 )}{( t ^{2} + 9 ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{8 t}{t ^{2} + 9})

定数を除去:

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

= 8 \frac{d}{d t} (\frac{t}{t ^{2} + 9})

商の法則を適用:

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

= 8 \cdot \frac{\frac{d t}{d t} ( t ^{2} + 9 ) - \frac{d}{d t} ( t ^{2} + 9 ) t}{( t ^{2} + 9 ) ^{2}}

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

\frac{d}{d t} (t^{2} + 9) = 2 t

= 8 \cdot \frac{1 \cdot ( t ^{2} + 9 ) - 2 tt}{( t ^{2} + 9 ) ^{2}}

簡素化

8 \cdot \frac{1 \cdot ( t ^{2} + 9 ) - 2 tt}{( t ^{2} + 9 ) ^{2}} : \frac{8 ( - t ^{2} + 9 )}{( t ^{2} + 9 ) ^{2}}

= \frac{8 ( - t ^{2} + 9 )}{( t ^{2} + 9 ) ^{2}}