derivative of |x|^a

解

\frac{d}{d x} (∣ x ∣^{a})

a x ∣ x ∣^{a - 2}

解答ステップ

\frac{d}{d x} (∣ x ∣^{a})

連鎖法則を適用:

a ∣ x ∣^{a - 1} \frac{d}{d x} (∣ x ∣)

= a ∣ x ∣^{a - 1} \frac{d}{d x} (∣ x ∣)

\frac{d}{d x} (∣ x ∣) = \frac{x}{∣ x ∣}

= a ∣ x ∣^{a - 1} \frac{x}{∣ x ∣}

簡素化

a ∣ x ∣^{a - 1} \frac{x}{∣ x ∣} : a x ∣ x ∣^{a - 2}

= a x ∣ x ∣^{a - 2}