derivative of (ln(x+y)^2)

解

\frac{d}{d x} ((ln (x + y))^{2})

\frac{2 ln ( x + y ) ( 1 + \frac{d y}{d x} )}{x + y}

解答ステップ

\frac{d}{d x} ((ln (x + y))^{2})

連鎖法則を適用:

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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