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人気のある微分積分 >

d/(dt)(t/(1+t))

解

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

解

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

解答ステップ

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

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

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

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

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

簡素化

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

グラフ

人気の例

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