derivative of 1/2 ln^2(x)

解

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

\frac{ln ( x )}{x}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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