derivative (800t)/(t+2)

解

導関数

\frac{800 t}{t + 2}

\frac{1600}{( t + 2 ) ^{2}}

解答ステップ

\frac{d}{d t} (\frac{800 t}{t + 2})

定数を除去:

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

= 800 \frac{d}{d t} (\frac{t}{t + 2})

商の法則を適用:

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

= 800 \cdot \frac{\frac{d t}{d t} ( t + 2 ) - \frac{d}{d t} ( t + 2 ) t}{( t + 2 ) ^{2}}

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

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

= 800 \cdot \frac{1 \cdot ( t + 2 ) - 1 \cdot t}{( t + 2 ) ^{2}}

簡素化

800 \cdot \frac{1 \cdot ( t + 2 ) - 1 \cdot t}{( t + 2 ) ^{2}} : \frac{1600}{( t + 2 ) ^{2}}

= \frac{1600}{( t + 2 ) ^{2}}