derivative of sqrt((x^2-1/(x^2-2x+1)))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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