derivative of ln(xln(x)ln(x))

解

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

\frac{3 ln ^{2} ( x )}{x}

解答ステップ

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

簡素化

ln (x) ln (x) ln (x) : ln^{3} (x)

= \frac{d}{d x} (ln^{3} (x))

連鎖法則を適用:

3 (ln (x))^{2} \frac{d}{d x} (ln (x))

= 3 (ln (x))^{2} \frac{d}{d x} (ln (x))

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

= 3 (ln (x))^{2} \frac{1}{x}

簡素化

3 ln^{2} (x) \frac{1}{x} : \frac{3 ln ^{2} ( x )}{x}

= \frac{3 ln ^{2} ( x )}{x}