derivative derivative of 1/((ln(x)))

解

導関数

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

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

解答ステップ

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

指数の規則を適用する:

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

= \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}

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

簡素化

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

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