derivative of ln|ln(x|)

解

\frac{d}{d x} (ln ∣ ln (x) ∣)

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

解答ステップ

\frac{d}{d x} (ln ∣ ln (x) ∣)

連鎖法則を適用:

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

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

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

= \frac{1}{∣ ln ( x ) ∣} \cdot \frac{ln ( x )}{x ∣ ln ( x ) ∣}

簡素化

\frac{1}{∣ ln ( x ) ∣} \cdot \frac{ln ( x )}{x ∣ ln ( x ) ∣} : \frac{1}{x ln ( x )}

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