derivative sqrt((y+1)/(y-1))

解

導関数

\frac{y + 1}{y - 1}

- \frac{1}{y + 1 ( y - 1 ) ^{\frac{3}{2}}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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