derivative of ln(1-2/x)

解

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

\frac{2}{x ( x - 2 )}

解答ステップ

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

連鎖法則を適用:

\frac{1}{1 - \frac{2}{x}} \frac{d}{d x} (1 - \frac{2}{x})

= \frac{1}{1 - \frac{2}{x}} \frac{d}{d x} (1 - \frac{2}{x})

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

= \frac{1}{1 - \frac{2}{x}} \cdot \frac{2}{x ^{2}}

簡素化

\frac{1}{1 - \frac{2}{x}} \cdot \frac{2}{x ^{2}} : \frac{2}{x ( x - 2 )}

= \frac{2}{x ( x - 2 )}