derivative of 4/x-x(x+1)

解

\frac{d}{d x} (\frac{4}{x} - x (x + 1))

- \frac{4}{x ^{2}} - 2 x - 1

解答ステップ

\frac{d}{d x} (\frac{4}{x} - x (x + 1))

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{4}{x}) - \frac{d}{d x} (x (x + 1))

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

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

= - \frac{4}{x ^{2}} - (2 x + 1)

簡素化

= - \frac{4}{x ^{2}} - 2 x - 1