derivative of |x|^3

解答

\frac{d}{d x} (∣ x ∣^{3})

\frac{3 x ^{3}}{∣ x ∣}

求解步骤

\frac{d}{d x} (∣ x ∣^{3})

使用连锁律:

3 ∣ x ∣^{2} \frac{d}{d x} (∣ x ∣)

= 3 ∣ x ∣^{2} \frac{d}{d x} (∣ x ∣)

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

= 3 ∣ x ∣^{2} \frac{x}{∣ x ∣}

化简

3 ∣ x ∣^{2} \frac{x}{∣ x ∣} : \frac{3 x ^{3}}{∣ x ∣}

= \frac{3 x ^{3}}{∣ x ∣}

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