derivative y=(400)/x+7+1/5 x

解

導関数

y = \frac{400}{x} + 7 + \frac{1}{5} x

- \frac{400}{x ^{2}} + \frac{1}{5}

解答ステップ

\frac{d}{d x} (\frac{400}{x} + 7 + \frac{1}{5} x)

簡素化

\frac{400}{x} + 7 + \frac{1}{5} x : \frac{400}{x} + 7 + \frac{x}{5}

= \frac{d}{d x} (\frac{400}{x} + 7 + \frac{x}{5})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{400}{x}) + \frac{d}{d x} (7) + \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{400}{x}) = - \frac{400}{x ^{2}}

\frac{d}{d x} (7) = 0

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= - \frac{400}{x ^{2}} + 0 + \frac{1}{5}

簡素化

= - \frac{400}{x ^{2}} + \frac{1}{5}