derivative of 2x-(2000/(x^2))

解

\frac{d}{d x} (2 x - \frac{2000}{x ^{2}})

2 + \frac{4000}{x ^{3}}

解答ステップ

\frac{d}{d x} (2 x - \frac{2000}{x ^{2}})

和/差の法則を適用:

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

= \frac{d}{d x} (2 x) - \frac{d}{d x} (\frac{2000}{x ^{2}})

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

\frac{d}{d x} (\frac{2000}{x ^{2}}) = - \frac{4000}{x ^{3}}

= 2 - (- \frac{4000}{x ^{3}})

簡素化

= 2 + \frac{4000}{x ^{3}}