What is the derivative of |x^3| ?

The derivative of |x^3| is (3x^5)/(|x^3|)

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

The first derivative of |x^3| is (3x^5)/(|x^3|)

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\frac{d}{d x} (x^{3})

\frac{3 x ^{5}}{∣ x ^{3} ∣}

Solution steps

\frac{d}{d x} (x^{3})

Apply the chain rule:

\frac{x ^{3}}{∣ x ^{3} ∣} \frac{d}{d x} (x^{3})

= \frac{x ^{3}}{∣ x ^{3} ∣} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{x ^{3}}{∣ x ^{3} ∣} \cdot 3 x^{2}

Simplify

\frac{x ^{3}}{∣ x ^{3} ∣} \cdot 3 x^{2} : \frac{3 x ^{5}}{∣ x ^{3} ∣}

= \frac{3 x ^{5}}{∣ x ^{3} ∣}

\int_{- 1}^{1} 2 - ∣ x ∣ - x^{4} d x

\frac{d y}{d x} = y^{4} sin (x)

\int \frac{2 ( 2 t - 1 )}{t ( 3 t ^{2} + 4 t - 1 )} d t

\int \frac{3 x}{x ^{2} + x + 1} d x

x e^{(x + 2)}

What is the derivative of |x^3| ?
The derivative of |x^3| is (3x^5)/(|x^3|)
What is the first derivative of |x^3| ?
The first derivative of |x^3| is (3x^5)/(|x^3|)