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

解

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

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

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (\frac{x}{4}), g = x - 4

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

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

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

= \frac{1}{x} (x - 4) + 1 \cdot ln (\frac{x}{4})

簡素化

\frac{1}{x} (x - 4) + 1 \cdot ln (\frac{x}{4}) : \frac{x - 4}{x} + ln (\frac{x}{4})

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