derivative of sqrt(5/x-1)

解

\frac{d}{d x} (\frac{5}{x} - 1)

- \frac{5}{2 x ^{\frac{3}{2}} - x + 5}

解答ステップ

\frac{d}{d x} (\frac{5}{x} - 1)

連鎖法則を適用:

\frac{1}{2 \frac{5}{x} - 1} \frac{d}{d x} (\frac{5}{x} - 1)

= \frac{1}{2 \frac{5}{x} - 1} \frac{d}{d x} (\frac{5}{x} - 1)

\frac{d}{d x} (\frac{5}{x} - 1) = - \frac{5}{x ^{2}}

= \frac{1}{2 \frac{5}{x} - 1} (- \frac{5}{x ^{2}})

簡素化

\frac{1}{2 \frac{5}{x} - 1} (- \frac{5}{x ^{2}}) : - \frac{5}{2 x ^{\frac{3}{2}} - x + 5}

= - \frac{5}{2 x ^{\frac{3}{2}} - x + 5}