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人気のある微分積分 >

derivative 7/(ln(x))

解

derivative

解

- \frac{7}{x ln ^{2} ( x )}

解答ステップ

\frac{d}{d x} (\frac{7}{ln ( x )})

定数を除去:

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

= 7 \frac{d}{d x} (\frac{1}{ln ( x )})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= 7 \frac{d}{d x} (ln^{- 1} (x))

連鎖法則を適用:

- \frac{1}{( ln ( x ) ) ^{2}} \frac{d}{d x} (ln (x))

= - \frac{1}{( ln ( x ) ) ^{2}} \frac{d}{d x} (ln (x))

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

= 7 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

簡素化

7 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{7}{x ln ^{2} ( x )}

= - \frac{7}{x ln ^{2} ( x )}

グラフ

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