derivative of (x+2((300)/x+4))

解

\frac{d}{d x} ((x + 2) (\frac{300}{x} + 4))

- \frac{600}{x ^{2}} + 4

解答ステップ

\frac{d}{d x} ((x + 2) (\frac{300}{x} + 4))

簡素化

(x + 2) (\frac{300}{x} + 4) : 4 x + \frac{600}{x} + 308

= \frac{d}{d x} (4 x + \frac{600}{x} + 308)

和/差の法則を適用:

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

= \frac{d}{d x} (4 x) + \frac{d}{d x} (\frac{600}{x}) + \frac{d}{d x} (308)

\frac{d}{d x} (4 x) = 4

\frac{d}{d x} (\frac{600}{x}) = - \frac{600}{x ^{2}}

\frac{d}{d x} (308) = 0

= 4 - \frac{600}{x ^{2}} + 0

簡素化

= - \frac{600}{x ^{2}} + 4