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人気のある微分積分 >

derivative log_{10}(1-x)

解

導関数

lo g_{10} (1 - x)

解

- \frac{1}{ln ( 10 ) ( 1 - x )}

解答ステップ

\frac{d}{d x} (lo g_{10} (1 - x))

対数の規則を適用する:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 1 - x )}{ln ( 10 )})

定数を除去:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (1 - x))

連鎖法則を適用:

\frac{1}{1 - x} \frac{d}{d x} (1 - x)

= \frac{1}{1 - x} \frac{d}{d x} (1 - x)

\frac{d}{d x} (1 - x) = - 1

= \frac{1}{ln ( 10 )} \cdot \frac{1}{1 - x} (- 1)

簡素化

\frac{1}{ln ( 10 )} \cdot \frac{1}{1 - x} (- 1) : - \frac{1}{ln ( 10 ) ( 1 - x )}

= - \frac{1}{ln ( 10 ) ( 1 - x )}

グラフ

人気の例

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