derivative of (c(200+(50)/x+(x^2)/5))

解

\frac{d}{d x} ((c) (200 + \frac{50}{x} + \frac{x ^{2}}{5}))

c (\frac{2 x}{5} - \frac{50}{x ^{2}})

解答ステップ

\frac{d}{d x} ((c) (200 + \frac{50}{x} + \frac{x ^{2}}{5}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= c \frac{d}{d x} (200 + \frac{50}{x} + \frac{x ^{2}}{5})

和/差の法則を適用:

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

= c (\frac{d}{d x} (200) + \frac{d}{d x} (\frac{50}{x}) + \frac{d}{d x} (\frac{x ^{2}}{5}))

\frac{d}{d x} (200) = 0

\frac{d}{d x} (\frac{50}{x}) = - \frac{50}{x ^{2}}

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

= c (0 - \frac{50}{x ^{2}} + \frac{2 x}{5})

簡素化

= c (\frac{2 x}{5} - \frac{50}{x ^{2}})