derivative f(x)=ln((x-2)/(x+1))

解

導関数

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

\frac{3}{( x - 2 ) ( x + 1 )}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x - 2}{x + 1}) = \frac{3}{( x + 1 ) ^{2}}

= \frac{1}{\frac{x - 2}{x + 1}} \cdot \frac{3}{( x + 1 ) ^{2}}

簡素化

\frac{1}{\frac{x - 2}{x + 1}} \cdot \frac{3}{( x + 1 ) ^{2}} : \frac{3}{( x - 2 ) ( x + 1 )}

= \frac{3}{( x - 2 ) ( x + 1 )}