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人気のある微分積分 >

derivative of x/(5+x)

解

\frac{d}{d x} (\frac{x}{5 + x})

解

\frac{5}{( 5 + x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{5 + x})

商の法則を適用:

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

= \frac{\frac{d x}{d x} ( 5 + x ) - \frac{d}{d x} ( 5 + x ) x}{( 5 + x ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (5 + x) = 1

= \frac{1 \cdot ( 5 + x ) - 1 \cdot x}{( 5 + x ) ^{2}}

簡素化

= \frac{5}{( 5 + x ) ^{2}}

グラフ

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