What is the derivative of |x|^3 ?

The derivative of |x|^3 is (3x^3)/(|x|)

What is the first derivative of |x|^3 ?

The first derivative of |x|^3 is (3x^3)/(|x|)

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\frac{d}{d x} (∣ x ∣^{3})

\frac{3 x ^{3}}{∣ x ∣}

Solution steps

\frac{d}{d x} (∣ x ∣^{3})

Apply the chain rule:

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 ∣}

Simplify

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

= \frac{3 x ^{3}}{∣ x ∣}

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n = 1 \sum \infty ln (1 + \frac{1}{n})

What is the derivative of |x|^3 ?
The derivative of |x|^3 is (3x^3)/(|x|)
What is the first derivative of |x|^3 ?
The first derivative of |x|^3 is (3x^3)/(|x|)