derivative sqrt((x+3)/(x-3))

解

導関数

\frac{x + 3}{x - 3}

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

解答ステップ

\frac{d}{d x} (\frac{x + 3}{x - 3})

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 3}) = - \frac{6}{( x - 3 ) ^{2}}

= \frac{1}{2 \frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}})

簡素化

\frac{1}{2 \frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{3}{x + 3 ( x - 3 ) ^{\frac{3}{2}}}

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