(1/(x(ln(x))^2))^'

解

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

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

解答ステップ

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

指数の規則を適用する:

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

= ((x (ln (x))^{2})^{- 1})^{^{'}}

連鎖法則を適用:

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

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

(x (ln (x))^{2})^{'} = ln^{2} (x) + 2 ln (x)

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

簡素化

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

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