derivative of ln(((1-x)/(1+x)))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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