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

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (ln (\frac{x}{4})) = \frac{1}{x}

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