derivative of ln((2-x/(2+x)))

解

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

- \frac{4}{( - x + 2 ) ( x + 2 )}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{2 - x}{2 + x}) = - \frac{4}{( 2 + x ) ^{2}}

= \frac{1}{\frac{2 - x}{2 + x}} (- \frac{4}{( 2 + x ) ^{2}})

簡素化

\frac{1}{\frac{2 - x}{2 + x}} (- \frac{4}{( 2 + x ) ^{2}}) : - \frac{4}{( - x + 2 ) ( x + 2 )}

= - \frac{4}{( - x + 2 ) ( x + 2 )}