derivative of-x+8/x+1

解

\frac{d}{d x} (- x + \frac{8}{x} + 1)

- \frac{8}{x ^{2}} - 1

解答ステップ

\frac{d}{d x} (- x + \frac{8}{x} + 1)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d x}{d x} + \frac{d}{d x} (\frac{8}{x}) + \frac{d}{d x} (1)

\frac{d x}{d x} = 1

\frac{d}{d x} (\frac{8}{x}) = - \frac{8}{x ^{2}}

\frac{d}{d x} (1) = 0

= - 1 - \frac{8}{x ^{2}} + 0

簡素化

= - \frac{8}{x ^{2}} - 1