derivative of | x/3-1|

解

\frac{d}{d x} (\frac{x}{3} - 1)

\frac{x - 3}{3 ∣ x - 3 ∣}

解答ステップ

\frac{d}{d x} (\frac{x}{3} - 1)

連鎖法則を適用:

\frac{\frac{x}{3} - 1}{( \frac{x}{3} - 1 )} \frac{d}{d x} (\frac{x}{3} - 1)

= \frac{\frac{x}{3} - 1}{( \frac{x}{3} - 1 )} \frac{d}{d x} (\frac{x}{3} - 1)

\frac{d}{d x} (\frac{x}{3} - 1) = \frac{1}{3}

= \frac{\frac{x}{3} - 1}{( \frac{x}{3} - 1 )} \cdot \frac{1}{3}

簡素化

\frac{\frac{x}{3} - 1}{\frac{x}{3} - 1} \cdot \frac{1}{3} : \frac{x - 3}{3 ∣ x - 3 ∣}

= \frac{x - 3}{3 ∣ x - 3 ∣}